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Finding Distance in the Coordinate Plane Answers

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Which expression represents the distance between the points (a, 0) and (0, 5) on a coordinate grid?

A
StartRoot a squared + 5 EndRoot
Option A
B
StartRoot a squared + 25 EndRoot
Option B
C
StartRoot (a minus 25) squared EndRoot
Option C
D
StartRoot (a minus 5) squared EndRoot
Option D
2
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In a right triangle, the hypotenuse has endpoints XY, shown on the graph. If Z represents the third vertex in the triangle and is located in the second quadrant with integer coordinates, what is the length of YZ?

Question illustration
A
3
B
4
C
5
D
6
3

What is the length of segment XY?

Question illustration
A
4.5 units
B
units
Option B
C
units
Option C
D
9 units
4

Which expression can be used to determine the length of segment AB?

Question illustration
A
StartRoot 2 squared + 6 squared EndRoot
Option A
B
StartRoot 2 squared minus 6 squared EndRoot
Option B
C
StartRoot 6 squared minus 2 squared EndRoot
Option C
D
StartRoot (2 + 6) squared EndRoot
Option D
5

Which equation correctly shows how to determine the distance between the points (9, –2) and (6, 3) on a coordinate grid?

A
d = StartRoot (6 minus 3) squared + (9 minus (negative 2)) squared EndRoot
Option A
B
d = StartRoot (6 + 3) squared + (9 + (negative 2)) squared EndRoot
Option B
C
d = StartRoot (6 minus 9) squared + (3 minus (negative 2)) squared EndRoot
Option C
D
d = StartRoot (6 + 9) squared + (3 + (negative 2)) squared EndRoot
Option D
6

In a right triangle, the hypotenuse has endpoints P(–3, 2) and Q(1, –3).If R represents the third vertex in the triangle and R is located in the third quadrant, what is the length of PR?

Question illustration
A
3
B
4
C
5
D
6
7

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
8

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.
9

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
10

What is the length of segment RS?

Question illustration
A
StartRoot 65 EndRoot
Option A
B
12
C
13
D
StartRoot 153 EndRoot
Option D

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