Chapter 2 Diagnostic Test
STUDENT BOOK PAGES 68–71
1. Calculate each unknown side length. Round to two decimal places, if necessary.
b)
a)
2. Solve each equation. Round to one decimal place, if necessary.
2 − x x +1
c)
a) x2 + 25 = 169
+
=5
3
5
3
b) (2x + 1) – 3(5 – x) = 16
d) 85 = 16 + x2
4
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3. Determine the equation of the line that
a) passes through (5, –3) and (8, 6)
1
b) has a slope of − and passes through (4, 7)
2
c) is perpendicular to y = 2 – 3x and passes through (3, 1)
d) is parallel to 4x + 2y = 7 and passes through (–1, –4)
4. Determine the point of intersection for each pair of lines.
a) y = 3x + 5
b) 3y – x = 12
1
y = x – 15
2x + 4y = 7
2
5. Calculate the radius of the semicircle.
6. Which of these statements is not true?
a) A rectangle is a special type of parallelogram.
b) A square is a special type of rhombus.
c) A rhombus is a special type of square.
d) A rhombus is a special type of kite.
Chapter 2 Diagnostic Test |
1
Chapter 2 Diagnostic Test Answers
1. a) 1.5 cm
b) 6.23 m
2. a) 12 or –12
b) 6.7
c) –31
d) 8.3 or –8.3
3. a) y = 3x – 18
1
b) y = – x + 9
2
1
c) y = x
3
d) y = –2x – 6
4. a) (–8, –19)
b) (–2.7, 3.1)
5. about 17 cm
6. c)
Copyright © 2011 by Nelson Education Ltd.
If students have difficulty with the questions in the Diagnostic Test, you may need
to review the following topics:
• applying the Pythagorean theorem to determine side lengths of a right triangle
• determining the equation of a line given two points on the line
• determining the equation of a line given the y-intercept and the slope
• determining the point of intersection for a linear system
2 |
Principles of Mathematics 10: Chapter 2 Diagnostic Test Answers
Lesson 2.1 Extra Practice
STUDENT BOOK PAGES 72–80
1. Determine the coordinates of the midpoint of
each line segment.
2. A midpoint of a line segment is (3.5, –2), and
one endpoint is (1, 7).
a) Describe a strategy you could use to
determine the coordinates of the other
endpoint.
b) Apply your strategy to determine these
coordinates.
5. Determine the equation of the perpendicular
bisector of the line segment with each pair of
endpoints.
a) (3, 1) and (5, 5)
b) (–3, 2) and (5, –2)
c) (3, 3) and (7, 3)
6. The municipal councils of two cities agree that a
new airport will not be closer to one city than to
the other. The coordinates of the cities on a map
are A(23, 17) and B(47, 25). Describe all the
possible locations for the airport.
7. Quadrilateral PQRS has vertices at P(1, 7),
Q(6, 8), R(7, 1), and S(3, –1).
a) Determine the point of intersection for the
diagonals of this quadrilateral.
b) Determine the midpoint of each diagonal.
c) Is PQRS a parallelogram? Explain how you
know.
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3. a) The points (11, 4) and (–3, 2) are the
endpoints of a diameter of a circle.
Determine the coordinates of the centre of
the circle.
b) Another diameter of the same circle has
endpoint (–1, 8). Determine the coordinates
of the other endpoint.
4. Three of the vertices of rhombus ABCD are
A(5, 6), B(–2, 5), and C(3, 0).
a) What property of rhombuses can you use
to determine the coordinates of the fourth
vertex, D?
b) Determine the coordinates of D.
Lesson 2.1 Extra Practice |
3
Lesson 2.1 Extra Practice Answers
1. midpoint of AB: (3, 4)
midpoint of CD: (3.5, 1.5)
midpoint of EF: (–1, –0.5)
2. a) Use the midpoint formula to write an
equation for each coordinate:
x1 + x 2
y + y2
= 3.5 and 1
= −2 .
2
2
Substitute x1 = 1 and y2 = 7 into these
equations, and solve for x2 and y2.
b) (6, –11)
3. a) (4, 3)
b) (9, –2)
1
x +5
2
b) y = 2x – 2
c) x = 5
5. a) y = −
6. The airport can be located at any point on the
line with equation y = –3x + 126.
7. a) (4.5, 3.5)
b) midpoint of PR: (4, 4)
midpoint of QS: (4.5, 3.5)
c) No. The diagonals do not meet at a
common midpoint.
Copyright © 2011 by Nelson Education Ltd.
4. a) Opposites sides of a rhombus are parallel.
b) (10, 1)
4 |
Principles of Mathematics 10: Lesson 2.1 Extra Practice Answers
Lesson 2.2 Extra Practice
STUDENT BOOK PAGES 81–87
1. Determine the length of each line segment.
2. Calculate the distance between every possible
pair of points in the diagram.
4. Suppose that you are given the coordinates of
the endpoints of a line segment. Describe the
most efficient strategy you could use to
calculate both the slope and the length of the
line segment.
5. The walls of a room in an art gallery need to be
repainted. The coordinates of the corners of the
room, in metres, are (3, 8), (7, 7), (7, 1), (2, 2),
and (–1, 5). The room is 5 m high, and 1 L of
paint covers 35 m2. How much paint will be
needed, to the nearest tenth of a litre?
6. An optical fibre trunk runs in a straight line
through points (5, 20) and (45, 10) on a grid.
What is the minimum length of optical fibre that
is needed to connect the trunk to buildings at
(30, 35) and (10, 10), if 1 unit on the grid
represents 1 m? Round your answer to the
nearest tenth.
Copyright © 2011 by Nelson Education Ltd.
3. The coordinates of four possible sites for a
landfill are given below. Which site is farthest
from a town located at (4, 8)?
a) (0, 5) b) (7, 12) c) (6, 3) d) (8, 4)
Lesson 2.2 Extra Practice |
5
Lesson 2.2 Extra Practice Answers
1. PQ: 5.8 units; RS: about 4.1 units
TU: about 4.2 units
4. Answers may vary, e.g., determine x1 – x2 and
y1 – y2. For the slope, divide the second value
by the first value. For the length, square the
values, add them, and take the square root.
5. 3.5 L
6. 29.1 m
Copyright © 2011 by Nelson Education Ltd.
2. AB: about 4.5 units
AC: about 8.5 units
AD: about 3.6 units
BC: about 6.1 units
BD: about 6.1 units
CD: about 7.1 units
3. d)
6 |
Principles of Mathematics 10: Lesson 2.2 Extra Practice Answers
Lesson 2.3 Extra Practice
STUDENT BOOK PAGES 88–93
1. This table of values gives points that lie
on the same circle.
x
–7
y
±1
1
±5
±7
5
±1
a) Copy and complete the table.
b) Sketch the circle.
c) Write the equation of the circle.
2. For each equation of a circle:
i) Determine the diameter.
ii) Determine the x- and y-intercepts.
a) x2 + y2 = 625
b) x2 + y2 = 0.16
6. A satellite transfers from a near-Earth orbit,
with equation x2 + y2 = 51 122 500, in
kilometres, to another orbit that is 35 km higher.
How many kilometres longer, to two decimal
places, is the second orbit than the first?
7. A circle is centred at (0, 0) and passes through
point (16, –7). Determine the other endpoint of
the diameter through (16, –7). Explain your
strategy.
8. Points (a, –7) and (4, b) are on the circle with
equation x2 + y2 = 50. Determine the possible
values of a and b. Round to one decimal place,
if necessary.
3. A circle is centred at (0, 0) and passes through
point (–3, 7). Write the equation of the circle.
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4. Which of these points is not on the circle with
equation x2 + y2 = 225?
a) (14, 1) b) (12, –9) c) (0, 15) d) (9, 12)
5. a) Determine the radius of a circle that passes
through
i) (0, –6)
ii) (5, 12)
b) Write the equation of each circle in part a).
c) State the coordinates of two other points on
each circle.
Lesson 2.3 Extra Practice |
7
Lesson 2.3 Extra Practice Answers
1. a)
x
–7
–5
–1
1
5
7
y
±1
±5
±7
±7
±5
±1
b)
3. x2 + y2 = 58
4. a)
5. a) i) 6 units
ii) 13 units
b) i) x2 + y2 = 36
ii) x2 + y2 = 169
c) Answers may vary, e.g.,
i) (0, 6), (–6, 0)
ii) (13, 0), (–13, 0)
6. 219.91 km
c) x2 + y2 = 50
8. a = ±1, b = ±5.8
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2. a) i) 50 units
ii) x-intercepts: (25, 0), (–25, 0)
y-intercepts: (0, 25), (0, –25)
b) i) 0.8 units
ii) x-intercepts: (0.4, 0), (–0.4, 0)
y-intercepts: (0, 0.4), (0, –0.4)
7. (–16, 7); the diameter has midpoint (0, 0), so the
coordinates of the other endpoint are the
opposites of the coordinates of the given
endpoint.
8 |
Principles of Mathematics 10: Lesson 2.3 Extra Practice Answers
Chapter 2 Mid-Chapter Review Extra Practice
STUDENT BOOK PAGES 94–95
1. The midpoint of line segment AB is at
M(–5, 2.5). If endpoint A is at (–1, –3),
determine the coordinates of endpoint B.
2. Rectangle EFGH has vertices at E(1, 5), F(9, 7),
and G(8, 11). Determine the coordinates of the
fourth vertex, H.
3. A guide rope is laid out in three stages along the
ascent of a vertical rock face. The rope is
attached to the rock face at points (0, 0), (5, 3),
(–1, 12), and (3, 17), in that order. Determine
the total length of the rope, to the nearest tenth
of a metre.
6. Write the equation of a circle, centred at (0, 0),
that models each situation.
a) a G-training device for astronauts, with a
radius of 13 m
b) a wheel rim with a diameter of 16 in
7. A design for a kitchen tile uses circles and
squares, as shown. If the large square has side
lengths of 125 mm, what is the equation of the
small circle, assuming that its centre is at (0, 0)?
Round to the nearest millimetre.
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4. The Big Pumpkin, a restaurant and pie shop, is a
short distance from a major highway. The
highway passes, in a straight line, through
(–4, –2) and (8, 4) on a map. The Big Pumpkin
is located at (–1, 3). What is the shortest
distance from The Big Pumpkin to the highway,
to the nearest tenth of a kilometre, if 1 unit on
the map represents 1 km?
5. Two points, A(0.5, 2.5) and B(3.5, 3.5), lie on a
line. Point C(–0.5, 5.5) lies off to one side of the
line.
a) Use only the distance formula to show that
BC is not perpendicular to the line through A
and B.
b) Determine the distance from C to the line
through A and B. Do not calculate a point of
intersection.
Chapter 2 Mid-Chapter Review Extra Practice |
9
Chapter 2 Mid-Chapter Review Extra Practice Answers
1. (–9, 8)
2. (0, 9)
3. 23.1 m
6. a) x2 + y2 = 169
b) x2 + y2 = 64
7. x2 + y2 = 1953, or x2 + y2 = 1954
4. 3.1 km
5. a) Answers may vary, e.g., AC = 10 = 3.16
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or about 3.2 units and BC = 2 5 = 4.47 or
about 4.5 units so BC is not the minimum
distance from C to AB. Therefore, BC is not
perpendicular to AB.
1
b) Answers may vary, e.g., the slope of AB =
3
and the slope of AC = –3, which means that
AC is perpendicular to AB. The distance from
C to AB is the length of AC, which is about
3.2 units.
10 |
Principles of Mathematics 10: Chapter 2 Mid-Chapter Review Extra Practice Answers
Lesson 2.4 Extra Practice
STUDENT BOOK PAGES 96–103
1. Quadrilateral ABCD has two sides that measure
5 units and two sides that measure 2.5 units.
What types of quadrilateral could ABCD be?
For each type, make a possible sketch of ABCD
on a grid.
2. P(–3, 2), Q(2, 3), and R(–2, 7) are the vertices
of a triangle.
a) Show that +PQR is an isosceles triangle.
b) Is +PQR also a right triangle? Justify your
answer.
3. a) Describe a strategy you could use to decide
whether a quadrilateral is a rhombus, if you
are given the coordinates of its vertices.
b) Use your strategy to show that polygon
JKLM, with vertices at J(–5, 3), K(3, 1),
L(5, –7), and M(–3, –5), is a rhombus.
6. A rhombus is a special type of kite and also a
special type of parallelogram. How would you
apply this description of a rhombus if you were
using the coordinates of the vertices of a
quadrilateral to determine the type of
quadrilateral? Include examples in your
explanation.
7. The corners of a new park have the coordinates
S(–5, 1), T(5, –4), U(1, –5), and V(–5, –2) on a
map. What shape is the park? Include your
calculations in your answer.
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4. In quadrilateral EFGH, EF = 7.5 cm and
FG = 5.5 cm. The slopes of EF, FG, and GH are
1
4, , and 4, respectively.
4
a) What must be true about the slope and length
of EH if EFGH is a parallelogram?
b) Could the length of GH equal 7.5 cm if
EFGH is an isosceles trapezoid? Explain.
5. Two vertices of +ABC, an isosceles right
triangle, are located at A(2, 1) and B(5, –2).
Determine all the possible locations of C if
a) AB is a side of+ABC that is not the
hypotenuse
b) AB is the hypotenuse
Lesson 2.4 Extra Practice |
11
Lesson 2.4 Extra Practice Answers
5. a) (5, 4), (–1, –2), (8, 1), or (2, –5)
b) (2, –2) or (5, 1)
1. Answers may vary, e.g.,
parallelogram
6. Answers may vary, e.g., I would use the
distance formula to determine the lengths
of all the sides. If two pairs of adjacent
sides are congruent, then the quadrilateral
is a kite; e.g., A(–3, 3), B(1, 5), C(7, 3),
D(1, 1). I would use the slope formula to
determine the slopes of all the sides. If the
slopes of opposite sides are equal, then the
quadrilateral is a parallelogram; e.g.,
E(1, 2), F(4, 5), G(8, 5), H(5, 2). If the
quadrilateral is both a kite and a
parallelogram, then it is a rhombus; e.g.,
J(1, 1), K(4, 6), L(7, 1), M(4, –4).
rectangle
kite
7. ST = 5 5 = 11.18 units,
2. a) PQ = PQ = 26 = 5.10 units,
PR = PR = 26 = 5.10 units
b) No. Answers may vary, e.g., mPQ =
1
,
5
mPR = 5, and mQR = –1; none of the
slopes are negative reciprocals.
3. a) Determine all four side lengths, and check
whether they are equal.
b) JK = KL = LM = JM = 2 17 = 8.25 units
UV = 3 5 = 6.71 units, SV = 3 units;
since the side lengths are all different, the
park is not a parallelogram, kite, or
isosceles trapezoid.
1
1
1
mST = − , mTU = , mUV = − , mSV is
2
4
2
undefined; since the park has one parallel
pair of sides, it is a (non-isosceles)
trapezoid.
1
, EH = 5.5 cm
4
b) No. Since EF and GH are the parallel
sides in the isosceles trapezoid, they
cannot be the same length.
4. a) mEH =
12 |
Principles of Mathematics 10: Lesson 2.4 Extra Practice Answers
Copyright © 2011 by Nelson Education Ltd.
TU = 17 = 4.12 units,
Lesson 2.5 Extra Practice
STUDENT BOOK PAGES 104–110
1. a) Rectangle ABCD has vertices at A(–3, 1),
B(0, –2), C(5, 3), and D(2, 6). Show that the
diagonals are the same length.
b) Give an example of a quadrilateral that is not
a rectangle but has diagonals that are the
same length.
5. a) Show that points A(5, –5), B(–5, 5), C(1, 7),
and D(–7, –1) lie on the circle with equation
x2 + y2 = 50.
b) Show that AB is a diameter of the circle.
c) Show that AB is the perpendicular bisector of
chord CD.
2. a) Show that the diagonals of quadrilateral
EFGH bisect each other at right angles.
6. A trapezoid has vertices at J(–4, 4), K(0, 7),
L(8, 3), and M(8, –2).
a) Show that the line segment joining the
midpoints of JK and LM bisects the line
segment joining the midpoints of JM and KL.
b) Show that the two line segments described in
part a) are perpendicular.
c) Based on your answer for part b), make a
conjecture about trapezoid JKLM. Use
analytic geometry to determine whether your
conjecture is true.
b) Make a conjecture about the type of
quadrilateral in part a). Use analytic
geometry to explain why your conjecture is
either true or false.
3. Kite PQRS has vertices at P(–3, 3), Q(2, 3),
R(1, –5), and S(–6, –1). Show that the
midsegments of this kite form a rectangle.
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4. Show that the diagonals of the kite in question 3
are perpendicular, and that diagonal PR bisects
diagonal QS.
7. +XYZ has vertices at X(3, 5), Y(3, –2), and
Z(–3, –4). Verify that the area of the
parallelogram formed by joining the midpoints
of the sides of +XYZ and the vertex X is half the
area of +XYZ.
Lesson 2.5 Extra Practice |
13
Lesson 2.5 Extra Practice Answers
BD = 2 17 = 8.25 units
b) Answers may vary, e.g., a quadrilateral
with vertices at (0, 2), (4, 0), (0, –6), and
(–4, 0): both diagonals have a length of
8 units, but the quadrilateral is not a
rectangle.
1
2. a) mEG = − and mFH = 3, so EG and FH are
3
perpendicular; MEG = (1.5, 2.5) = MFH, so
EG and FH bisect each other.
b) Answers may vary, e.g., conjecture: EFGH
is a rhombus.
EF = FG = GH = EH = 5 units, so my
conjecture is correct.
3. Answers may vary, e.g., MPQ = (–0.5, 3),
MQR = (1.5, –1), MRS = (–2.5, –3),
MPS = (–4.5, 1); the slopes of the four
1
1
midsegments are –2, , –2, and , so
2
2
adjacent midsegments are perpendicular.
Therefore, the midsegments form a rectangle.
4. Answers may vary, e.g., mPR = –2 and
1
mQS = , so the diagonals are perpendicular.
2
The equation of the line through PR is
y = –2x – 3, and MQS = (–2, 1) lies on this line
(check by substitution). Therefore, PR
intersects QS at its midpoint.
6. a) Answers may vary, e.g., MJK = (–2, 5.5)
and MLM = (8, 0.5), so the equation of the
line through MJK and MLM is
1
9
y = − x + . MKL = (4, 5) and
2
2
MJM = (2, 1), so the midpoint of MKL and
1
9
MJM is (3, 3), which lies on y = − x +
2
2
(check by substitution). Therefore,
MJKMLM intersects MKLMJM at its midpoint,
i.e., MJKMLM bisects MKLMJM.
1
b) The slope of MJK M LM = − and the slope
2
of MKLMJM = 2, so MJKMLM and MKLMJM
are perpendicular.
c) Answers may vary, e.g., conjecture:
trapezoid JKLM is isosceles. Since
1
mKL = − = mJM and JK = 5 = LM, my
2
conjecture is correct.
7. Answers may vary, e.g., the parallelogram
has vertices at X(3, 5), MXY = (3, 1.5),
MYZ = (0, –3), and MXZ = (0, 0.5). Let XMXY
be the base of the parallelogram, so the base
length is 3.5 units, the height is 3 units, and
the area of the parallelogram is 10.5 square
units. Let XY be the base of +XYZ, so the
base length is 7 units, the height is 6 units,
and the area is 21 square units. Therefore,
the area of the parallelogram is half the area
of +XYZ.
5. a) For A(5, –5), 52 + (–5)2 = 50; for B(–5, 5),
(–5)2 + 52 = 50; for C(1, 7), 12 + 72 = 50;
for D(–7, –1), (–7)2 + (–1)2 = 50; the points
lie on the circle.
b) MAB = (0, 0), which is the centre of the
circle, so AB is a diameter.
c) Answers may vary, e.g., mAB = –1 and
mCD = 1, so AB and CD are perpendicular.
The equation of the line through AB is
y = –x. MCD = (–3, 3), so MCD lies on this
diagonal (check by substitution) and
therefore AB intersects CD at its midpoint,
i.e., AB is the perpendicular bisector
of CD.
14 |
Principles of Mathematics 10: Lesson 2.5 Extra Practice Answers
Copyright © 2011 by Nelson Education Ltd.
1. a) AC = 2 17 = 8.25 units,
Lesson 2.7 Extra Practice
STUDENT BOOK PAGES 115–121
1. In +ABC, the altitude from vertex B meets AC
at point D.
a) Determine the equation of the line that
contains AC.
b) Determine the equation of the line that
contains BD.
c) Determine the coordinates of point D.
d) Determine the area of +ABC, to the nearest
whole unit.
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2. A fountain is going to be constructed in a park,
an equal distance from each of the three
entrances to the park. The entrances are located
at P(2, 9), Q(11, 6), and R(3, 2). Where should
the fountain be constructed?
4. A circle with radius r is centred at (0, 0). The
circle has a horizontal chord, AB, with endpoints
A(–h, k) and B(h, k) and a vertical diameter, CD,
with endpoints C(0, –r) and D(0, r).
a) Draw a diagram of the circle, showing AB,
CD, and their point of intersection, E.
Include expressions for the lengths of the line
segments in your diagram.
b) Use properties of the intersecting chords of a
circle to verify that the coordinates of A and
B satisfy the equation of the circle.
5. Classify the triangle that is formed by the lines
y = 2x + 3, x + 2y = 16, and 3y – x – 4 = 0
a) by its angles
b) by its sides
6. The arch of a bridge, which forms an arc of a
circle, is modelled on a grid. The supports are
located at (–15, 0) and (15, 0), and the highest
part of the arch is located at (0, 9). What is the
radius of the arch, if each unit on the grid
represents 1 m?
3. +XYZ has vertices at X(6, 5), Y(4, 1), and
Z(–2, 1).
a) Determine the equation of the perpendicular
bisector of XY.
b) Points P, Q, and R are on the perpendicular
bisector from part a). Determine the
coordinates of these points that make the
distances PX, QY, and RZ as short as
possible.
c) Point S is also on the perpendicular bisector
from part a). Determine the coordinates of S
that make the distances SX, SY, and SZ equal.
Lesson 2.7 Extra Practice |
15
Lesson 2.7 Extra Practice Answers
1. a) y = −3x + 2
1
1
b) y = x +
3
3
c) (0.5, 0.5)
d) 15 square units
5. a) right triangle
b) isosceles
6. 17 m
2. (6, 6)
3. a) y = –0.5x + 5.5
b) P(5, 3), Q(5, 3), R(0.2, 5. 4)
c) S(1, 5)
4. a)
b) ( AE )( BE ) = (CE )( DE )
(h)(h) = ( r − k )(r + k )
h2 = r 2 − k 2
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h2 + k 2 = r 2
16 |
Principles of Mathematics 10: Lesson 2.7 Extra Practice Answers
Chapter 2 Review Extra Practice
STUDENT BOOK PAGES 122–125
1. Show that the line defined by x + 2y = 0 is the
perpendicular bisector of line segment AB, with
endpoints A(6, 2) and B(2, –6).
2. Rhombus CDEF has vertices at C(–2, 2),
D(1, 6), and E(5, 9).
a) Determine the coordinates of vertex F.
b) Determine the perimeter of the rhombus.
6. a) Show that +PQR, with vertices at P(1, 4),
Q(1, 9), and R(5, 1), is isosceles.
b) Suppose that M and N are the midpoints of
PQ and PR. Explain, without calculations,
why +MNP is also isosceles.
7. +XYZ has vertices as shown. Determine the
orthocentre of this triangle.
3. A sonar ping travels outward from a submarine
in a circular wave at 1550 m/s. Assuming that
the submarine is located at (0, 0), write an
equation for the sonar wave after 5 s.
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4. +ABC has vertices as shown. Determine
whether this triangle is isosceles, equilateral, or
scalene.
8. +DEF has vertices at D(10, 0), E(–5, k), and
F(–5, –k), where k is a positive number. The
circumcentre of +DEF is at (0, 0).
a) Determine the equation of the circle that
passes through D, E, and F.
b) Determine the value of k.
c) Determine whether +DEF is isosceles,
equilateral, or scalene. Explain your answer.
5. a) A quadrilateral is formed by the lines
y = x + 4, y – 2x + 3 = 0, 2y – x = 5, and a
fourth line. Explain why this quadrilateral
cannot be a parallelogram.
b) If the quadrilateral in part a) is a trapezoid,
what must be true about the fourth line?
Chapter 2 Review Extra Practice |
17
Chapter 2 Review Extra Practice Answers
1. Answers may vary, e.g., the slope of the line
1
defined by x + 2y = 0 is − , and mAB = 2, so
2
AB is perpendicular to the line. Since
MAB = (4, –2) lies on the line (check by
substitution), the line is the perpendicular
bisector of AB.
2. a) F(2, 5)
b) 20 units
3. x2 + y2 = 60 062 500
4. scalene
7. (5, 3)
8. a) x2 + y2 = 100
b) 5 3 or about 8.66
c) equilateral;
DE = 10 3 = 17.32 or about 17.3 units,
EF = 10 3 = 17.32 or about 17.3 units,
DF = 10 3 = 17.32 = or about 17.3 units
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5. Answers may vary, e.g.,
a) No two of the three given lines are parallel,
so it is impossible for both pairs of opposite
sides of the quadrilateral to be parallel.
b) The slope of the fourth line must be 1, 2,
1
or .
2
6. a) PQ = PR = 5 units, so +PQR is isosceles.
b) Answers may vary, e.g.,
1
1
MP = , PQ = , PR = NP, so +MNP is
2
2
isosceles.
18 |
Principles of Mathematics 10: Chapter 2 Review Extra Practice Answers