AnswersPre-Algebra BFinding Distance in the Coordinate Plane

Finding Distance in the Coordinate Plane — Unit test Answers

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Segment KJ shown below is the hypotenuse of isosceles right triangle JLK. What is the length of one of the congruent legs of JLK?

Question illustration
A
3
B
StartRoot 18 EndRoot
Option B
C
6
D
StartRoot 72 EndRoot
Option D
2
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Angelica calculated the distance between the two points shown on the graph below.Step 1: Use the point C(–4, –5) to make a right triangle with the 90 degree vertex at C.Step 2: Determine the lengths of the legs: AC = 6 and BC = 10.Step 3: Substitute the values into the Pythagorean theorem: .Step 4: Evaluate She states the length of AB is 8 units. Which best describes the accuracy of Angelica’s solution?

Question illustration
A
Angelica is correct.
B
Angelica made an error determining the location of the right angle. The right angle should be at (2, 5).
C
Angelica made an error counting the lengths of the legs of the right triangle. The lengths should be 7 and 11.
D
Angelica made an error substituting the values into the Pythagorean theorem. The equation should be .
Option D
3

Which simplified fraction represents ?

Question illustration
A
StartFraction 45 Over 99 EndFraction
Option A
B
StartFraction 99 Over 45 EndFraction
Option B
C
StartFraction 5 Over 11 EndFraction
Option C
D
StartFraction 11 Over 5 EndFraction
Option D
4

A ladder that is 14 feet long is placed against a building. The bottom of the ladder is 6 feet from the base of the building. In feet, how high up the side of the building is the top of the ladder? Round to the nearest tenth of a foot.

Question illustration
Answer not available
5

Which is the best estimate of to the nearest tenth?

Question illustration
A
6.8
B
6.9
C
7.0
D
7.1
6

Sam said the square root of a rational number must be a rational number. Jenna disagreed. She said that it is possible that the square root of a rational number can be irrational. Who is correct and why?

A
Jenna is correct because all square roots are irrational numbers.
B
Sam is correct because all square roots of rational numbers are rational. An example is .
Option B
C
Jenna is correct because not all square roots are rational. An example is
Option C
D
Sam is correct because the properties of square roots state that the square root of a rational number is a rational number.
7

What is the length of the hypotenuse of the triangle?

Question illustration
A
cm
Option A
B
cm
Option B
C
cm
Option C
D
cm
Option D
8

Carlos went to buy a television the same size as his friend’s. When he got to the store, he found that televisions are measured along the diagonal. Which equation will help him find the size he wants?

Question illustration
A
20 squared + 35 squared = d squared
Option A
B
d squared + 20 squared = 35 squared
Option B
C
d squared + 35 squared = 20 squared
Option C
D
35 squared minus 20 squared = d squared
Option D
9

Nadia says the hypotenuse of this right triangle has a length of 73 because the Pythagorean theorem states that .Which best describes Nadia’s solution?

Question illustration
A
She is correct because she applied the Pythagorean theorem properly and her arithmetic is accurate.
B
She is incorrect because she should have used 45 as the length of the hypotenuse.
C
She is incorrect because she should have squared each leg length and then found the sum.
D
She is correct because the hypotenuse is the longest side of the triangle.
10

Which point best approximates ?

Question illustration
A
A
B
B
C
C
D
D
11

Kendra is determining the distance between the points (6, 8) and (2, –3). Her work is shown below. Step 1: Step 2: Step 3: Step 4: Which best describes the accuracy of Kendra’s solution?

Question illustration
A
Her solution is correct.
B
Her solution is incorrect. She subtracted before squaring.
C
Her solution is incorrect. She made an error when substituting the x-values into the equation.
D
Her solution is incorrect. She made an error when substituting the y-values into the equation.
12

The values and are plotted on the number line.What is the approximate difference in tenths between and ?

Question illustration
A
0.3
B
0.7
C
1.3
D
2.2
13

A set of stairs is being built as shown. The length of each stair is 11 inches. What is the rise, r, for each stair? Round to the nearest inch.

Question illustration
A
2 inches
B
7 inches
C
17 inches
D
24 inches
14

Lewis needed to find the difference in lengths between the hypotenuse and the longest leg of this triangle. His work is shown below.What errors did Lewis make? Check all that apply.

Question illustration
A
He simplified incorrectly. It should be 20 instead of 200.
Option A
B
He found the difference between the hypotenuse and the short leg instead of the long leg.
C
He evaluated incorrectly. It should be .
Option C
D
He evaluated incorrectly. It should be .
Option D
E
He should not have taken the square root of each side to get rid of the exponent.
15

Which set of side lengths is a Pythagorean triple?

A
1, 3, 10
B
4, 5, 9
C
9, 40, 41
D
16, 30, 44
16

Which statements are true? Select the two correct answers.

A
The square root of a positive number greater than 1 is less than the number.
B
The square root of a positive number is always less than half of the number itself.
C
The square root of a positive number less than 1 is less than the number.
D
The square root of a perfect square is not a whole number.
E
The square root of a positive number less than 1 is between 0 and 1.
17

Which sets of side lengths represent Pythagorean triples? Check all that apply.

A
1, 2, 5
B
6, 8, 14
C
8, 15, 17
D
10, 24, 26
E
15, 20, 30
F
28, 45, 53
18

Which is a perfect square?

A
72
B
81
C
90
D
99
19

What is the length of segment AC?

Question illustration
Answer not available
20

Which is the correct classification and decimal expansion of ?

Question illustration
A
irrational number,
Option A
B
irrational number,
Option B
C
rational number,
Option C
D
rational number,
Option D

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