Name _________________________________________ Date ______________ Block ________
Parallel/Perpendicular Lines and Distance/Midpoint
Take-Home Test
1. What is the slope of a line that is perpendicular to
y = -3x + 4.
5. What is the equation of the line that is perpendicular
to this line and passes through (-6, -2)?
2. What is the y-intercept of the equation 3x – 2y = 24?
6. What is the equation of the line that is parallel to line
m and passes through (8, -7)?
3. Monica graphed the line y = 3x + 2. Janice graphs a
second line that is parallel to Monica’s and passes through
(-2, 0). What is the equation of Janice’s line?
7. Mario drew this line below. He wants to draw a second
line that is parallel to the first and passes through (4, -5).
What is the equation of Mario’s second line?
1
1
5
8
4. The equation of line k is 𝑦 = − 𝑥 − . What is the
equation of the line that is perpendicular to line k and
passes through (0,0)?
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8. What is the slope of a line parallel to the line
6x – 4y = 12?
13. Name the slope and y-intercept of y = 2x – 1. Then
graph the line.
9. Line f contains the points (5, -4) and (4, -6). What is
the slope of a line perpendicular to it?
14. Name a point on and the slope of y – 3 = -2(x + 5).
Graph the line. Then tell an equation of ANY line that
would be perpendicular to it.
Tell whether each pair of lines is parallel, perpendicular,
or neither.
10. y + 3x = -2; 3x + 2y = 12
15. Line j passes through points (-6, 1) and (-3, 6). Line m
is parallel to line j and passes through point (15, -1). What
is the equation of line m?
11. 2x – 7y = -42; 4y = -7x – 2
Write the equation for (a) the horizontal line and
(b) the vertical line that contain the given point.
12. y = 3; x = -2
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16. B(4, 9)
17. C(-2, -3)
18. Find the coordinates of the midpoint of the segment
whose endpoints are H(5,2) and K(3,10).
23. Julia created the coordinate grid below to identify the
locations of her house and her friend Carol’s house. Julia’s
house is located at (155, 102). Carol’s house is located at
(493, 388).
19. Find the distance between points P(5,8) and Q(3,9) to
the nearest tenth.
20. Find the coordinates of the midpoint of the segment
whose endpoints are H(8,1) and K(4,7).
21. Find the distance between points P(-2,1) and Q(-10,7)
to the nearest tenth.
22. The Frostburg-Truth bus travels from Frostburg Mall
through the City Center to Sojourner Truth Park. The mall
is 4 miles west and 5 miles south of the City Center. Truth
Park is 4 miles east and 2 miles north of the Center. How
far is it from Truth Park to the Mall to the nearest tenth
of a mile?
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A.) What are the coordinates of the midpoint between the
girls’ houses? Show all your work.
B.) There is a straight path between the girls’ houses. If
Julia and Carol meet at the midpoint between their
houses, what distance would each girl have to walk? Round
the answer to the nearest yard. Show all you work.
24. A high school soccer team is going to Columbus to see
a professional soccer game. A coordinate grid is
superimposed on a highway map of Ohio. The high school is
at point (3, 4) and the stadium in Columbus is at point
(7, 1). The map shows a highway rest stop halfway between
the cities. What are the coordinates of the rest stop?
What is the approximate distance between the high school
and the stadium? (One unit 4.2 miles.)
25. Plot A at (0,3), B at (7,7) and C at (7,3).
26. Each unit on the map represents 5 miles. What is the
actual distance from Oceanfront to Seaside?
y
8
6
Seaside
4
2
–8 –6 –4 –2
–2
Landview
–4
2
4
6
8
x
Oceanfront
–6
–8
A) What is the length of AB?
A.
B.
C.
D.
10 miles
50 miles
about 8 miles
about 40 miles
B) What is the length of BC?
C) What is the length of AC?
D) What is the perimeter of the triangle?
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27. You live in Worland, Wyoming, which has approximate
(latitude, longitude) coordinates of (44N, 88W). Your
friend lives in Portland, Maine, with coordinates of
(44N, 70W). You plan to meet halfway between the two
cities. Find the coordinates of the halfway point.