Finding Distance on a Coordinate Grid

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?

• 3

• 4

• 5

• 6

The hypotenuse of right triangle ABC is represented by segment AB, as shown on the graph.

At which point could point C be located?

• (-3,3)

• (-3,2)

• (5,-5)

• (5,-3)

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?

• 3

• 4

• 5

• 6

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

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What is the length of segment XY?

• 4.5 units

• 9 units

What is the length of segment GH?

• 8 units

• 12 units

Segment KJ shown below is the hypotenuse of isosceles right triangle JLK.

What is the length of one of the congruent legs of JLK?

• 3

• 6

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

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In the formula above, how does each subtraction expression relate to the Pythagorean theorem?

• Each subtraction expression represents the length of one leg of a right triangle with a hypotenuse of length d.

• Each subtraction expression represents the length of the hypotenuse of a right triangle with a leg of length d.

• Each subtraction expression represents half the length of the hypotenuse of a right triangle with a hypotenuse of length d.

• Each subtraction expression represents the square of the length of the hypotenuse of a right triangle with a hypotenuse of length d.

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

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