Pythagorean Theorem and Distance Formula

Milestones Review

​Distance Formula and Pythagorean Theorem

Distance can be found by drawing a right triangle,

THEN

Find the length of the hypotenuse by using Pythagorean theorem.

Find the distance between two points.

a²+b²=c²

where a and b are the legs and c is the hypotenuse.

Let's find the distance between (-3, 3) and (2, 1).

Find the distance between two points.

a²+b²=c²

where a and b are the legs and c is the hypotenuse.

Let's find the distance between (-3, 3) and (2, 1).

Find the distance between two points.

​SOLUTION

Fill in the Blanks

Multiple Choice

Find the distance between the 2 points.

• 9.7

• 10.7

• 11.7

• 12.7

Multiple Choice

Find the distance between point A and B.

• 7.1

• 7.8

• 8.7

• 8.9

What if the points aren't on a graph?

These are the lengths of the legs.

Example (-2, 4) and (4, 5)

x's The difference of 4 and -2 is 6. This is a.

y's The difference of 4 and 5 is 1. This is b.

1²+6²=c²

Find the difference between the x's and y's

Then draw the right triangle like we just practiced.

Graph them yourself

Multiple Choice

Find the distance between ( 1, 3) and (5, 6) 

• 3

• 4

• 5

• 6

Multiple Choice

Find the distance between (3, 24) and (7, 56).

• 32.1

• 32.2

• 32.3

• 32.4

Multiple Choice

Find the distance between (-4, 5) and (7, 18).

• 15.96

• 16.08

• 16.23

• 17.03

Multiple Choice

The Pythagorean Theorem ONLY works on which triangle?

• obtuse

• scalene

• isosceles

• right

Multiple Choice

What side(s) will always be the longest on a right triangle?

• The Hypotenuse

• Leg A

• Leg B

• The Right Angle

Multiple Choice

If three sides of a right triangle are 9, 40, and 41, which side is the hypotenuse?

• 9

• 40

• 41

Is it a Right Triangle?

Multiple Choice

Do these 3 side lengths form a right triangle?
13, 80, and 81?

• yes

• no

Multiple Choice

Do the segment lengths 9, 12, and 15 form a right triangle?

• Yes

• No

Multiple Choice

Find the missing side.

• 18

• 16

• 17

• 19

Multiple Choice

Find the missing side.

• 11

• 12

• 13

• 14

Multiple Choice

A triangle has legs that are 7 inches and 24 inches long. How long is the hypotenuse?

• 23

• 26

• 28

• 25

Multiple Choice

Which equation can be used to solve for "x"?

• 15² – x² = 21²

• x² – 15² = 21²

• 15² + 21² = x²

• 21² – 15² = x²

Multiple Choice

Find h

• 35.60

• 35.00

• 35.71

• 61.03

Word Problems

When solving word problems, it helps to draw a triangle and fill in the missing information.

Multiple Choice

Lisa drives her car 46 km south and then 13 km east. How far is she from her starting point?

• 44.1 km

• 59 km

• 47.8 km

• 33 km

Multiple Choice

A baseball "diamond" is actually a square with sides of 90 feet. If a runner tries to steal second base, how far must the catcher, at home plate, throw to get the runner "out"? (Distance across the diagonal)

• 180 feet

• 90 feet

• 13.4 feet

• 127.3 feet

Multiple Choice

The slide at the playground has a height of 6 feet. The base of the slide measured on the ground is 8 feet. What is the length of the slide?

• 8 feet

• 5.29 feet

• 10 feet

• 14 feet