Deck 11: The Geometry of Lines

Question 1

The bottom of a ladder sits on the ground 3 horizontal feet from a wall.The top of the ladder rests atop a wall that is 11 feet high.What is the slope of the line made by the ladder? (Assume that the positive direction points from the base of the ladder toward the wall.) ​

A) 4.02 feet per foot
B) 0.27 feet per foot
C) 3.67 feet per foot
D) 0.30 feet per foot

Answer 1

3.67 feet per foot

Question 2

The slope of a line is the run over the rise.

Answer 2

False

Question 3

Consider a line with slope 1.20.What rise corresponds to a run of 4 feet? ​

A) 4.80 feet
B) 0.30 feet
C) 3.33 feet
D) 5.61 feet

Answer 3

4.80 feet

Question 4

At the outside wall the roof is 10 feet high.The slope of the roof is 1.03 feet per foot.If the roof is extended beyond the outside wall, what is the height of the roof 3 horizontal feet from the outside wall toward the exterior of the room? ​

A) 13.82 feet
B) 6.91 feet
C) 7.84 feet
D) 13.09 feet

Question 5

A vertical line has a slope of 0.

Question 6

At the outside wall the roof is 9 feet high.The slope of the roof is 1.28 feet per foot.What is the height of the roof 4 horizontal feet from the outside wall toward the interior of the room? ​

A) 15.06 feet
B) 12.13 feet
C) 12.44 feet
D) 14.12 feet

Question 7

A ladder leans against a wall so that its slope is 3.61 feet per foot.The top of the ladder is 11 vertical feet above the ground.What is the horizontal distance from the base of the ladder to the wall? (Assume that the positive direction points from the base of the ladder toward the wall.) ​

A) 3.05 feet
B) 0.33 feet
C) 3.15 feet
D) 0.95 feet

Question 8

You are driving up a straight road.You pass a sign that says Elevation 1504 feet.Also, 3 horizontal miles further you see a sign that says Elevation 2829 feet.The peak of the mountain is 7 horizontal miles from the first sign.What is the elevation of the mountain? ​

A) 8105.00 feet
B) 4595.67 feet
C) 8105.59 feet
D) 4596.03 feet

Question 9

Take west to be the positive direction.You are driving in a westerly direction up a straight road.You pass a sign that says Elevation 1883 feet.Also, 5 horizontal miles further you see a sign that says Elevation 3350 feet.What is the slope of the road you are driving on? ​

A) 293.40 feet per mile
B) 670.00 feet per mile
C) 293.94 feet per mile
D) 670.86 feet per mile

Question 10

The rise of a line can be found by multiplying the run by the slope.

Question 11

Consider a line with slope 1.70.What run corresponds to rise of 5 feet? ​

A) 8.50 feet
B) 0.34 feet
C) 2.94 feet
D) 9.03 feet

Question 12

The bottom of a ladder sits on the ground 4 horizontal feet from a wall against which its top rests.The slope of the line made by the ladder is 3.37 feet per foot.What is the vertical height of the top of the ladder? (Assume that the positive direction points from the base of the ladder toward the wall.) ​

A) 8.14 feet
B) 13.48 feet
C) 7.37 feet
D) 14.01 feet

Question 13

The slope of a line tells the rate at which it rises or falls.

Question 14

For a certain line, a run of 5 feet corresponds to a rise of 7 feet.What is the slope of this line? ​

A) 1.40 feet
B) 0.71 feet
C) 1.03 feet
D) 1.53 feet

Question 15

If a line is represented on coordinate axes, then the horizontal intercept is the point where the line meets the horizontal axis.

Question 16

At the outside wall the roof is 8 feet high.Also, 5 horizontal feet from the outside wall toward the interior of the room, the roof is 11 feet tall.If the roof is extended beyond the outside wall, what is the height of the roof 5 horizontal feet from the outside wall toward the exterior of the room? ​

A) 5.80 feet
B) 5.73 feet
C) 5.00 feet
D) 6.26 feet

Question 17

At the outside wall the roof is 10 feet high.Also, 5 horizontal feet from the outside wall toward the interior of the room, the roof is 11 feet tall.What is the height of the roof 10 horizontal feet from the outside wall toward the interior of the room? ​

A) 12.10 feet
B) 14.55 feet
C) 15.22 feet
D) 12.00 feet

Question 18

Among lines with positive slope, a larger slope corresponds to a steeper line.

Question 19

The slope of a line tells how much the line rises for each unit of run.

Question 20

The slope of a line varies from point to point on the line.

Question 21

A line through has slope -1.5.What is the vertical intercept? ​

A) 10.03
B) 14.50
C) 15.07
D) 9.67

Question 22

A line through has slope 0.38.What is the horizontal intercept? ​

A) -9.37
B) 3.72
C) 3.82
D) -9.79

Question 23

What is the slope of the line through the points and ? ​

A) 0.45
B) -1.67
C) 1.33
D) -0.60

Question 24

A pipeline is to span a horizontal distance of 144 feet.But the pipeline is sloped downward to promote drainage.The pipeline drops by a total of 14 feet over that span.How much lower is the pipe at the end of each 12-foot horizontal stretch? ​

A) 1.64 feet
B) 0.10 feet
C) 0.56 feet
D) 1.17 feet

Question 25

The floor of a lake slopes downward in a straight line.The depth 27 feet from shore is 16 feet.At what distance from shore is the depth 40 feet? ​

A) 67.50 feet
B) 24.52 feet
C) 23.70 feet
D) 67.67 feet

Question 26

You are driving up a straight mountain road which has a slope of 75.00 feet per mile.If you are initially at an altitude of 791 feet and later at an altitude of 819 feet, how many horizontal miles have you driven? ​

A) 0.76 miles
B) 21.47 miles
C) 0.37 miles
D) 22.05 miles

Question 27

A line passes through the points and .For what ​y value does the point lie on the line? ​

A)
B) ​
C) ​
D) ​

Question 28

A vertical 5-foot pole casts a shadow that is 5 feet long.How long a shadow will a vertical 9-foot pole cast at the same time? ​

A) 9.00 feet
B) 9.59 feet
C) 9.000 feet
D) 9.86 feet

Question 29

A line passes through the point and has slope -2.62.For what ​x value does the point lie on the line? ​

A)
B)
C)
D)

Question 30

A line through has slope -0.62.What is the horizontal intercept? ​

A) 17.72
B) 10.96
C) 11.16
D) 17.68

Question 31

A line passes through the points and .For what ​x value does the point lie on the line? ​

A)
B)
C)
D)

Question 32

What is the slope of the line through the points and ? ​

A) 0.27
B) -0.75
C) 0.40
D) 0.75

Question 33

The floor of a lake slopes downward in a straight line.The depth 29 feet from shore is 12 feet.At what distance from shore is the depth 48 feet? ​

A) 116.00 feet
B) 20.78 feet
C) 19.86 feet
D) 116.57 feet

Question 34

A line through has slope 0.89.What is the vertical intercept? ​

A) -2.85
B) 2.66
C) 2.97
D) -2.99

Question 35

The floor of a lake slopes downward in a straight line.The depth 21 feet from shore is 18 feet.What is the depth 35 feet from shore? ​

A) 40.83 feet
B) 30.12 feet
C) 30.00 feet
D) 40.95 feet

Question 36

A vertical 6-foot pole casts a shadow that is 10 feet long.How tall is a vertical pole that casts a shadow that is 12 feet long at the same time? ​

A) 20.00 feet
B) 20.84 feet
C) 7.20 feet
D) 7.38 feet

Question 37

A line passes through the point and has slope 1.28.For what y value does the point lie on the line? ​

A)
B) ​
C) ​
D) ​

Question 38

You are driving up a straight mountain road which has a slope of 58.00 feet per mile.If you are initially at an altitude of 725 feet, what is your altitude after you drive 4 horizontal miles? ​

A) 957.66 feet
B) 787.00 feet
C) 957.00 feet
D) 787.27 feet

Question 39

Take west to be the positive direction.The height of a sloped roof above the place you are standing is 13 feet.If you move 5 feet to the west, the height is 7 feet.What is the slope of the roof line? ​

A) -1.20 feet
B) 1.20 feet
C) -0.63 feet
D) 1.61 feet

Question 40

The peak of a roof is 19 feet tall.At the outside wall, 14 horizontal feet away, the roof is 8 feet tall.If the roof line were extended until it struck the ground, how many horizontal feet from the outside wall would that occur? ​

A) 10.72 feet
B) 10.18 feet
C) 14.00 feet
D) 14.53 feet

Question 41

Your office window is 35 feet high.Looking out your window, you find that the top of a statue lines up exactly with the bottom of a building that is 600 horizontal feet from your office, as is shown in the figure below.The statue is 125 horizontal feet from the building.How tall is the statue?

A) 6.48 feet
B) 9.71 feet
C) 7.29 feet
D) 10 feet

Question 42

The figure below shows a simplified pattern for a wrap skirt that is 20 inches long and has a top hem of 57 inches.The bottom hem has a length of 63 inches.Suppose you decide to alter the pattern to make a wrap skirt with the same top hem length but a length of 27 inches.How long should be the bottom hem? ​

A) 65.51 inches
B) 64.05 inches
C) 63.17 inches
D) 65.10 inches

Question 43

At a distance 5 miles west of town, oil-bearing deposits are found 3066 feet deep.Also, 6 miles west of town, the oil is found 3257 feet down.Assuming the oil-bearing stratum lies on a straight line, how deep would you expect to drill 8 miles west of town in order to find oil? ​

A) 3448.00 feet
B) 3448.51 feet
C) 3639.91 feet
D) 3639.00 feet

Question 44

A surveyor whose eye is 6 feet above the ground views a mountain peak which is 2 horizontal miles distant.See the figure below.Directly in his line of sight is the top of a surveying pole which is 10 horizontal feet distant and 8 feet high.How tall is the mountain peak? Note: 1 mile is 5280 feet.

A) 5143 feet
B) 2118 feet
C) 2546 feet
D) 4798 feet

Question 45

An ice cream cone is 4 inches deep and 2 inches across the top, as shown in the figure below.If we wanted to make a king-size cone which has the same shape but is 2.5 inches across the top, how deep would the cone be? ​

A) 5 inches deep
B) 4.5 inches deep
C) 6 inches deep
D) 5.5 inches deep

Question 46

At a distance 5 miles west of town, oil-bearing deposits are found 3185 feet deep.Also, 8 miles west of town, the oil is found 3356 feet down.Assuming the oil-bearing stratum lies on a straight line, how far west of town would you expect to drill 3606 feet deep in order to find oil? ​

A) 12.39 miles
B) 13.10 miles
C) 10.38 miles
D) 9.39 miles