Download Triangles in Coordinate Plane

Geometry
Triangles in Coordinate Plane
Name ________________________________ Pd _____
For each triangle below, plot the points and then answer the questions that follow. Make sure to show all work!
1) A(1, 8), B(1, 2), C(9, 2)
a) What is the perimeter of ∆ABC?
b) Find sin A. Express your answer
as a simplified fraction.
c) Find mC. Round your answer
to the nearest tenth, if necessary.
e) Find the length of ̅̅̅̅̅
𝐴′𝐶′ if ABC is dilated by k = 3
d) Classify the triangle based on sides and angles.
Explain.
2) A(-6, -2), B(-3, -1), C(-1, -7)
a) What is the perimeter of ∆ABC?
b) What is the slope of a line parallel to ̅̅̅̅
𝐴𝐵? Perpendicular to ̅̅̅̅
𝐴𝐵?
𝐴𝐷
c) Place a point D on ̅̅̅̅
𝐴𝐶 such that 𝐷𝐶 =
2
3
d) Transform ∆ABC using the composite transformation below. Graph and label each figure of the composite
transformation. Then, determine the ordered pairs of your final coordinates.
•
•
Rotate 180 about the origin
Reflect over y = x
A” (
,
)
B” (
,
)
C” (
,
)
3) A(5, -1), B(9, -1), C(9, -5)
a) What is the perimeter of ∆ABC?
b) Find tan A. Express your answer
as a simplified fraction.
c) Find mC. Round your answer
to the nearest tenth, if necessary.
e) Find the length of ̅̅̅̅̅̅
𝐴′𝐵′ if ∆ABC is dilated by k = 2
d) Classify ∆ABC based on sides and angles. Explain.
4) A(-6, 1), B(-3, 7), C(0, 3)
a) What is the slope of a line parallel to ̅̅̅̅
𝐴𝐵? Perpendicular to ̅̅̅̅
𝐴𝐵?
𝐴𝐷
1
̅̅̅̅ so that
b) Place a point D on 𝐴𝐵
=2
𝐷𝐵
c) What is the perimeter of ∆ABC?
D) Transform ∆ABC using the composite transformation below. Graph and label each figure of the composite
transformation. Then, determine the ordered pairs of your final coordinates.
•
•
Translate (x, y)→(x + 6, y)
Rotate 90 clockwise around origin
A” (
,
)
B” (
,
)
C” (
,
)
5) A(-5, 6), B(-5, 1), C(7, 1)
a) What is the perimeter of ∆ABC?
b) Find cos A. Express your
answer as a simplified
fraction.
c) Find mC. Round your
answer to the nearest.
tenth, if necessary
̅̅̅̅̅ if ∆ABC is dilated by k = ½
e) Find the length of 𝐴′𝐶′
d) Which other expression also equals cos A?
i) sin B
ii) sin C
iii) cos B
iv) cos C
6) A(-8, -1), B(-2, -3), C(-6, -5)
̅̅̅̅ ? Perpendicular to 𝐴𝐶
̅̅̅̅ ?
a) What is the slope of a line parallel to 𝐴𝐶
b) Which angle is a right angle? Explain.
Hint: Think about what has to be true for two lines to create a right angle.
𝐴𝐷
1
c) Place a point D on ̅̅̅̅
𝐴𝐵 so that 𝐷𝐵 = 3
d) Transform ∆ABC using the composite transformation below. Graph and label each figure of the composite
transformation. Then, determine the ordered pairs of your final coordinates.
•
•
Reflect over the y-axis
Translate (x, y)→(x - 4, y + 8)
A” (
,
)
B” (
,
)
C” (
,
)
7) A(1, 6), B(6, 2), C(-2, -8)
a) What is the perimeter ∆ABC?
b) Find cos A. Express your
answer as a simplified
fraction.
c) Find mC. Round your
answer to the nearest.
tenth, if necessary
1
d) Find the length of ̅̅̅̅̅
𝐴′𝐶′ if ∆ABC is dilated by k = 3
̅̅̅̅?
e) What is the slope of a line parallel to 𝐴𝐵
̅̅̅̅?
Perpendicular to 𝐴𝐵
8) A(4, -4), B(6, 0), C(0, 3)
̅̅̅̅? Perpendicular to 𝐴𝐵
̅̅̅̅?
a) What is the slope of a line parallel to 𝐴𝐵
b) Which angle is a right angle? Explain.
Hint: Think about what has to be true for two lines to create a right angle.
𝐶𝐷
2
c) Place a point D on ̅̅̅̅
𝐶𝐵 so that 𝐷𝐵 = 1
d) Transform ∆ABC using the composite transformation below. Graph and label each figure of the composite
transformation. Then, determine the ordered pairs of your final coordinates.
•
•
Dilate by k = 2
Rotate 180 about the origin
A” (
,
)
B” (
,
)
C” (
,
)