U6 – W4
Parallel and Perpendicular Lines Worksheet
1. Graph each pair of lines on the same coordinate grid. Find their slopes and conclude whether the lines are
parallel, perpendicular, or neither.
a) 𝑦 = 2𝑥 + 5 𝑎𝑛𝑑 4𝑥 − 2𝑦 + 6 = 0
b) 𝑦 =
1
𝑥
2
− 4 𝑎𝑛𝑑 𝑥 + 2𝑦 + 2 = 0
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
2
4
6
8 10
-10 -8 -6 -4 -2
2
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
c) 𝑦 = 3 𝑎𝑛𝑑 𝑥 = −2
6
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d) 𝑦 = 3𝑥 𝑎𝑛𝑑 𝑥 + 3𝑦 − 6 = 0
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
4
2
4
6
8 10
-10 -8 -6 -4 -2
2
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
4
6
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2. The slopes of two lines are given. Conclude whether the lines are parallel, perpendicular, or neither. Justify
your answers.
2
4
3
−4
a) 𝑚 = 𝑎𝑛𝑑 𝑚 =
b) 𝑚 = 𝑎𝑛𝑑 𝑚 =
c) 𝑚 = 2 𝑎𝑛𝑑 𝑚 = −2
3
6
d) 𝑚 = 1 𝑎𝑛𝑑 𝑚 = −1
4
e) 𝑚 =
1
5
3
𝑎𝑛𝑑 𝑚 = 0.2
1
4
f) 𝑚 = 2 4 𝑎𝑛𝑑 𝑚 = − 9
3. What is the slope of a line that is parallel to each line?
3
a) 𝑦 = 5 𝑥 − 2
b) 𝑦 = −𝑥 + 7
c) 2𝑥 − 𝑦 + 3 = 0
mparallel = _______
mparalllel = _________
mparallel = ________
mperpendicular = ________ mperpendicular = _________
mperpendicular = _________
d) 4𝑥 + 3𝑦 = 12
mparallel = _______
mperpendicular = ________
e) y = 2
mparalllel = _________
mperpendicular = _________
f) x = -5
mparallel = ________
mperpendicular = _________
4. Write the equations of two lines that are parallel to the line 3x - 6y - 5 = 0.
5. Write the equations of two lines that are perpendicular to the line 4x + y - 2 = 0.
6. In each of the following, line k and l pass through the given points. Determine if k and l are parallel,
perpendicular, or neither. (HINT: Compare the slopes of k and l
a) k: (2, 3) & (4, 4); l (3, 6) & (-7, 1)
b) k: (2, 5) & (4, 11); l (0, 4) & (-9, 7)
c) k: (4, 3) & (6, 7); l (-2, 1) & (0, 0)
d) k: (-3, -7) & (9, -7); l (3, 5) & (-1, 4)
e) k: (5, 8) & (5, -2); l (-2, 5) & (-2, -1)
f) k: (-5, -1) & (-1, 5); l (3, 4) & (7, -2)
10
7. A triangle has vertices A(1, 2), B(3, 8), and C(6, 7).
a) Plot these points and draw the triangle.
8
b) Does this appear to be a right triangle? Explain.
4
6
2
c) Find the slopes of the line segments that form this triangle.
-10 -8 -6 -4 -2
2
4
6
-2
-4
-6
-8
-10
d) Explain how the slopes can be used to conclude whether or not this is a right triangle. Is it?
8. Determine whether or not the following sets of points form right triangles. Justify your answers with
mathematical reasoning.
a) A(1, 1), B(-2, 5), C(3, -2)
b) P(2, 4), Q(-2, 2), R(5, -2)
Answer Key: 1a) parallel b) neither c) perpendicular d) perpendicular 2a) parallel, same slope
b) perpendicular, negative reciprocals c) neither d) perpendicular, negative reciprocals e) parallel, same
slope f) perpendicular, negative reciprocals 3a) 3/5 and -5/3 b) -1 and 1 c) 2 and -1/2
d) -4/3 and ¾ e) 0 and undefined f) undefined and 0 4. Must have slope = ½ 5. Must have slope of ¼
6a) parallel b) perpendicular c) perpendicular d) neither e) parallel f) neither
7b) yes, two lines look like they form a 900 angle c) mAB = 3, mBC = -1/3, mAC = 1 d) AB is perpendicular to BC
8a) mAB = -4/3, mBC = -7/5, mAC = -3/2 NO b) mPQ = 1/2, mQR = -4/7, mRP = -2
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