Practice Page
Directions: These questions pertain to situations requiring the use of equations of parallel or perpendicular lines. Read carefully and choose the best answer.

1.
Assuming the bookcase at the right was constructed in a normal, usable manner, which of the sets of lines could represent the equations of coplanar lines m and n respectively in a coordinate plane?
 bookcase
Choose:
 
y = x + 1; y = -½x + 1
  y = -1; y = 5
  y = ½x; y=2x
  y = -1; x = 5



2.
The support arm, ab, is perpendicular to a line tangent to this curve on a roller coaster at the point of tangency B. The equation of the tangent line to the curve at B is 3x + 2y = 28. Find the equation of the support arm, ab.
rollercoaster
Lines perpendicular to tangents to curves, at the point of tangency, are referred to as "normals".
Choose:
 
coaster1
 
coaster3
  coaster4
  coaster2



3.
The line through points B and C is tangent to circle A at point B. What is the equation of the tangent line bc ?
circletangent
Choose:
 
circlemath2
 
circlemath1
  circlemath3
  circlemath4



4.
A line through point (-6,4) is perpendicular to the line y = ½x + 2. Find the equation of the line through point (-6,4).
appmath1
Choose:
 
y = -½x + 7
 
y = -½x + 1
  y = -2x - 8
  y = -2x + 16



5.
The staircase shown at the right is constructed in normal fashion, with a step rise of 6 inches. Lines p and q follow the tread of the steps and are parallel. Line t follows the rise of the step. Which of the following choices states the equations of lines p, q and t in that order?
stairsAssume that the coordinate grid
represents each unit as one inch.
Choose:
 
y = 8, y = 3, x = 2
 
y = 9, y = 3, x = 2
  x = 2, x = 8, y = 3
  x = 2, x = 6, y = 3



6.
A rectangular barn is positioned on a grid as shown. A contractor, installing a light pole at point P, wants to run the shortest underground conduit (pipe) possible to reach the barn.
a) Find the coordinates of the point where the pipe hits the barn.
Choose:
 
(5, 4.5)
(4.5, 4)
 
(4.4, 4.2)
(4.2, 4.6)

barnEach unit of the grid = 10 feet.
 
b) Find the length of the ditch needed to bury the pipe to the barn. Round answer to the nearest foot.
Choose:
 
5 feet
26 feet
54 feet
260 feet



7.
A question asks you to prove that the triangle shown on the graph is a right triangle using perpendicularity. ΔABC has A(-2,3), B(0,-3) and C(3,-2).

Which of the following statements could be used to verify that ΔABC is a right triangle?
app7
 
Choose:
 
The slope of ab7 is 3 and the slope of bc7 is -1/3, making the sides ⊥, ∠B a right angle and ΔABC a right triangle.
 
By observation, ΔABC has a right angle at B making ab7 perpendicular to bc7.
 
The slope of ab7 is -3 and the slope of bc7 is 1/3, making the sides ⊥, ∠B a right angle and ΔABC a right triangle.
 
By counting, AB is twice BC, making the sides perpendicular.



8.
A fabric designer tells you that the grid equation 2x + 4y = 8 represents a stripe in a new flannel fabric. She wants you to program the machine to place another parallel stripe crossing 4 units below the intersection of the axes. What equation will you enter into the machine to create this new stripe?
gg4
  Choose:  
 
      2x + y= - 4
x + 2y = -8
 
     -2x + y = - 4
-x + 2y = -8



9.
Which linear equation through (-2,2) will create a right angle when it intersects with the line shown on the graph?
(Points with integer coordinates are shown.)
perpgraph

Choose:
 
y - 2 = -1(x - 2)
 
y = x - 2
 
y = -x
 
y = -x - 2



10.
Which of the following linear equations have the same rate of change as the line seen in the graph at the right?
(Check all that apply, and hit SUBMIT!)
 

y - 1 = -½(x + 3)

y = 2x + 7

y - 4 = 3(x - 2)

x + 2y = 8

-x + 2y = 2

2y = -x

y + 8 = 2(x + 4)

        

parallelchoice
(Points with integer coordinates are shown.)

 

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