Warm Up
Use the coordinate plane provided to answer each question.
y
8
6
4
2
0
28 26 24 22
2
4
6
8
x
22
24
26
28
1. Plot points A (26, 22) and B (26, 28).
2. Is the distance between points A and B considered a horizontal distance, a vertical distance, or a
diagonal distance? Explain your reasoning.
3. How do you calculate the distance between points A and B?
4. What is the distance between points A and B?
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© 2012 Carnegie Learning
5. How do the negative coordinates affect the distance between points A and B?
12.1 Translating and Constructing Line Segments 651C
Check for Students’ Understanding
Use the given sides in each question.
P
Q
R
P
1. Construct a segment twice the length of segment PQ.
2. Construct triangle PQR.
3. Do you suppose everyone in your class constructed the same triangle? Explain your reasoning.
4. Your classmate was absent from school today and she is on the phone asking you how to duplicate
a line segment. What will you tell her?
© 2012 Carnegie Learning
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12.1 Translating and Constructing Line Segments 666A
5. Use the coordinate plane provided to answer each question. One unit represents one kilometer.
y
8
6
4
2
0
28 26 24 22
2
4
6
8
x
22
24
26
28
Vita’s house is located at point A (9, 7). Her dog wandered away from home, but fortunately, the dog was
wearing an identification tag which included Vita’s phone number. Vita received a phone call that the dog
was last seen at a location described by point B (27, 29).
How far did the dog wander from its home?
© 2012 Carnegie Learning
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666B Chapter 12 Geometry on the Coordinate Plane
Warm Up
1. What is the value of the point half-way between points P and T?
P
27
T
0
11
2. Bill insists the answer to Question 1 must be a positive answer. Is Bill correct? Explain his reasoning.
3. What is the value of the point half-way between points R and W?
R
6
0
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12
W
216
12.2 Midpoints and Bisectors 667C
4. Describe how you determined the value of the point half-way between two points in Questions 3.
5. What determines if the value of the point half-way between two points on a number line is positive
number or a negative number?
© 2012 Carnegie Learning
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667D Chapter 12 Geometry on the Coordinate Plane
Check for Students’ Understanding
1. Graph the three points on the coordinate plane.
A (210, 3), B (24, 3), C (27, 11)
y
12
9
6
3
0
212 29 26 23
3
6
9
12
x
23
26
29
212
2. Connect the three points to form triangle ABC.
3. Solve for the coordinates of M1, the midpoint of side AC.
4. Solve for the coordinates of M2, the midpoint of side BC.
5. Connect the two midpoints M1 and M2.
6. Calculate the distance between points M1 and M2.
680 Chapter 12 Geometry on the Coordinate Plane
© 2012 Carnegie Learning
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7. Calculate the distance between points A and B.
8. Compare the length of the midsegment (line segment M1M2) of a triangle to the length of the base of
the triangle (line segment AB).
© 2012 Carnegie Learning
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12.2 Midpoints and Bisectors 680A
Warm Up
Use the coordinate plane to answer each question.
y
8
6
4
2
0
28 26 24 22
2
4
6
8
x
22
24
26
28
1. Plot points A (26, 22), B (26, 28) and C (0, 28).
2. If angle B appears to be a right angle. Is this enough to conclude the measure of angle B is equal to
90 degrees? Explain your reasoning.
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3. How can the distance formula and the Pythagorean Theorem be helpful in determining that the
measure of angle B is equal to 90 degrees?
12.3 Translating and Constructing Angles and Angle Bisectors 681C
Check for Students’ Understanding
Use the given sides and angles in each question.
P
Q
R
P
P
1. Construct an angle twice the measure of angle P.
2. Construct triangle PQR.
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© 2012 Carnegie Learning
3. Do you suppose everyone in your class constructed the same triangle? Explain your reasoning.
4. A classmate was absent from school today and she is on the phone asking you how to duplicate an
angle. What will you tell her?
12.3 Translating and Constructing Angles and Angle Bisectors 688A
Warm Up
Graph each equation.
1. y 5 2x 1 5
2. y 5 22x 1 1
y
y
8
8
6
6
4
4
2
2
0
28 26 24 22
2
4
6
8
x
28 26 24 22
22
22
24
24
26
26
28
28
3. 3x 1 2y 5 8
2
4
6
8
0
2
4
6
8
x
4. 9x 2 4y 5 212
y
y
8
8
6
6
4
4
2
2
0
28 26 24 22
© 2012 Carnegie Learning
0
2
4
6
8
x
28 26 24 22
22
22
24
24
26
26
28
28
12.4 Parallel and Perpendicular Lines on the Coordinate Plane x
12
689C
Check for Students’ Understanding
Designing A Parking Lot
• Use graph paper to design a parking lot that is 150 feet by 400 feet.
• Maximize the number of cars in the parking lot.
• Describe how to paint the lines in the parking lot.
© 2012 Carnegie Learning
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12.4 Parallel and Perpendicular Lines on the Coordinate Plane 698A
Warm Up
1. Determine if line AB is perpendicular to line BC. State your reasoning.
y
8
6
B
C
A
2
0
28 26 24 22
2
4
6
8
x
22
24
26
28
Line AB contains points A (21, 3) and B (0, 5).
Line BC contains point B (0, 5) and C (2, 4).
© 2012 Carnegie Learning
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12.5 Constructing Perpendicular Lines, Parallel Lines, and Polygons 699C
2. Determine if line AB is parallel to line CD. State your reasoning.
y
8
6
B
A
2
D
0
28 26 24 22
22
2
4
6
8
x
C
24
26
28
Line AB contains points A (21, 3) and B (0, 5).
Line CD contains point C (0, 23) and D (2, 1).
© 2012 Carnegie Learning
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699D Chapter 12 Geometry on the Coordinate Plane
Check for Students’ Understanding
Given the radius of the circle and a starter line, construct a regular hexagon using only three arcs or
circles.
© 2012 Carnegie Learning
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12.5 Constructing Perpendicular Lines, Parallel Lines, and Polygons 708A