Name _________________________
Coordinate Geometry
Study Island
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1. The vertices of a quadrilateral are listed below.
A(7,-1), B(11,-1), C(13,-5), D(7,-5)
Which of the following is the strongest
classification that identifies this quadrilateral?
A. The quadrilateral is a trapezoid.
B. The quadrilateral is a rhombus.
C. The quadrilateral is a rectangle.
D. The quadrilateral is a square.
2. The vertices of a triangle are listed below.
H(3, 4), I(6, 2), J(3, -2)
What is the area of the triangle?
A. 9 square units
4. The vertices of hexagon PQRSTU are listed
below.
P(7, 8), Q(8, 5), R(8, 2), S(7, -1), T(6, 2), U(6, 5)
What is the approximate perimeter of the hexagon?
A. 9.32 units
B. 37.3 units
C. 15.49 units
D. 18.65 units
5. Let AB be the directed line segment beginning at
point A(1 , 3) and ending at point B(9 , -11). Find
the point P on the line segment that partitions the
line segment into the segments AP and PB at a ratio
of 1:1.
A.
B. 14.6 square units
C. 4.5 square units
B.
D. 18 square units
C.
3. Ethan wants to purchase a rectangular lot at a
lake resort. He drew the layout of the lot on a
coordinate plane, where the x- and y-values
represent the length, in yards.
The center of the lot is located at (0, 0).
The NE corner of the lot is located at (16.5, 13.5).
The SE corner of the lot is located at (16.5, -13.5).
The NW corner of the lot is located at (-16.5, 13.5).
The SW corner of the lot is located at (-16.5, -13.5).
What is the area of the rectangular lot?
A. 1,782 square yards
B. 120 square yards
C. 891 square yards
D. 445.5 square yards
D.
6. The vertices of quadrilateral LMNO are listed
below.
L(2, 6), M(10, -2), N(2, -10), O(-6, -2)
What is the approximate perimeter of the
quadrilateral?
A. 22.62 units
B. 127.92 units
C. 33.93 units
D. 45.24 units
Name _________________________
Coordinate Geometry
9. Teresa is visiting the arboretum to take
photographs for her photography class. At the
arboretum, there is a triangular water fountain
which she would like to photograph. Suppose her
location and the location of the water fountain are
plotted on the coordinate plane, where the x- and yvalues represent the position, in feet, from Teresa's
location, which is located at (0, 0). The locations of
the corners of the water fountain are as follows.
7.
A.
B.
C.
D.
8. The vertices of a rectangle are listed below.
Q(4, 5), R(6, 3), S(0, -3), T(-2, -1)
What is the area of the rectangle?
A. 12 square units
B. 24 square units
C. 48 square units
The northern corner of the water fountain is located
at (-5, 3).
The western corner of the water fountain is located
at (-13, -3).
The southern corner of the water fountain is located
at (-5, -9).
What is the perimeter of the water fountain?
A. 32 feet
B. 11 feet
C. 51 feet
D. 96 feet
D. 22.6 square units
10. The vertices of a triangle are listed below.
A(-5,5), B(-13,-1), C(-5,-7)
hich of the following correctly classifies the
triangle?
A. The triangle is an acute isosceles triangle.
B. The triangle is a right scalene triangle.
C. The triangle is a right isosceles triangle.
D. The triangle is an acute equilateral triangle.
Name _________________________
Coordinate Geometry
Answers
The height of triangle HIJ is the perpendicular
distance from point I to HJ. The height is
represented by IK on the graph above.
1. A
2. A
3. C
4. D
5. B
6. D
7. B
8. B
9. A
10. A
Next, use the distance formula to find the length of
the base, HJ, and the height, IK, of the triangle.
Length Calculation
Length
Base
HJ
Height
IK
Explanations
Then, calculate the area of the triangle.
1. Find the slope of each side of the quadrilateral.
Therefore, the area of the triangle is 9 square units.
3. First, sketch a picture of the lot on a coordinate
plane.
The two sides that have a slope of zero are
horizontal.
The side that has an undefined slope is vertical.
So, this shape has only one pair of opposite sides
that are parallel.
Therefore, the quadrilateral is a trapezoid.
2. First, graph triangle HIJ.
Next, use the distance formula to find the length of
two adjacent sides of the rectangular lot.
Side
NW
to NE
NE to
SE
Length Calculation
Length
Name _________________________
Coordinate Geometry
Then, find the area of the rectangular lot.
Therefore, the area of the rectangular lot is 891
square yards.
4. First, find the length of the sides of the hexagon
by using the distance formula.
Side
Length Calculation
Length
PQ
So, the desired point P is located at
QR
6. First, find the length of the sides of the
quadrilateral by using the distance formula.
RS
Side
ST
LM
TU
MN
UP
NO
Length Calculation
.
Length
OL
Next, to find the perimeter of the hexagon, calculate
the sum of the side lengths.
Next, to find the perimeter of the quadrilateral,
calculate the sum of the side lengths.
Therefore, the perimeter of the hexagon is
approximately 18.65 units.
5. Given a directed line segment AB starting at A(x1
, y1) and ending at B(x2 , y2), the point P(xp , yp) that
separates the line segment into the new line
segments AP and PB at a ratio of h:k is given by the
formulas shown below. Use the information given
in the question to calculate the coordinates of P.
Therefore, the perimeter of the quadrilateral is
approximately 45.24 units.
7.
8. First, use the distance formula to find the length
of two adjacent sides of the rectangle.
Side
Length Calculation
Length
Name _________________________
QR
RS
Next, find the area of the rectangle.
Therefore, the area of the rectangle is 24 square
units.
9. First, calculate the length, in feet, of each side of
the water fountain using the distance formula.
Then, find the perimeter.
Therefore, the perimeter of the water fountain is
32 feet.
10. Use the distance formula to find the length of
each side of the triangle.
Since two sides have the same length, the triangle is
isosceles.
Where a, b, and c are the lengths of the sides and c
is the longest side,
if c2 < a2 + b2, then it is an acute triangle,
if c2 = a2 + b2, then it is a right triangle, and
if c2 > a2 + b2, then it is an obtuse triangle.
Since the square of the longest side is less than the
sum of the squares of the other two sides, the
triangle is acute.
Therefore, the triangle is an acute isosceles
triangle.
Coordinate Geometry