11, yx 22 , yx

2 2

2 1 2 1( ) ( )D x x y y

The Distance Formula

Example Find the distance between (1, 4) and (-2, 3). Round to the nearest hundredths.

D = 3.16

2

12

2

12 )()(D yyxx

22 )43()12(D

22 )1()3(D

19D

10D

Example

Find the distance between the points, (10, 5) and (40, 45). Round to the nearest hundredths.

2

12

2

12 )()(D yyxx

22 )545()1040(D

22 )40()30(D

1600900D

2500D

D = 50

3. Find the distance between the points.

Round to the nearest tenths.

( ) ( )4 1 2 02 2

9 4

13

212

2

12 yyxx

4. Find the distance between the points.

Round to the nearest tenths.

212

2

12 yyxx

Pythagorean Theorem

2 2 2leg leg hyp

Pythagorean Theorem Word Problems

• A square has a diagonal with length of

20 cm. What is the measure of each

side? Round to the nearest tenths.

x = 14.1 cm

Pythagorean Theorem Word Problems

• A 25 foot ladder is leaning against a

building. The foot of the ladder is 15

feet from the base of the building.

How high is the top of the ladder

along the building? Round to the

nearest tenths.

x = 20 ft

Pythagorean Theorem Word Problems

• Ashley travels 42 miles east, then 19

miles south. How far is Ashley from

the starting point? Round to the

nearest tenths.

x = 46.1 miles

Pythagorean Theorem Word Problems

• What is the length of the altitude of an

equilateral triangle if a side is 12 cm?

Round to the nearest tenths.

x = 10.4 cm

Classwork Round to the nearest tenths.

Worksheet

Classwork / Homework Quadrilaterals Task

Conclusions Parallel

• Same slope

means sides are

parallel

• Opposite

reciprocal slopes

mean

perpendicular

segments (90)

Distance

• Same distance

means segments

are congruent