Pythagorean Theorem, Distance Formula and Midpoint Formula · Theorem, Distance Formula and...

Pythagorean Theorem, Distance

Formula and Midpoint Formula

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.

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.

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.

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.

11, yx 22 , yx

2 2

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

The Distance Formula

Given two points:

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

Midpoint Given 2 ordered pairs, it’s

the

AVG of the x’s and

AVG of the y’s.

Midpoint Formula

1 2 1 2,2 2

x x y y

Find the midpoint.

1. (3, 7) and (-2, 4)

2. (5, -2) and (6, 14)

(.5, 5.5)

(5.5, 6)

Find the midpoint.

3. (3, -9) and (14, 16)

4. (12, 17) and (-7, 9)

(8.5, 3.5)

(2.5, 13)

Find the midpoint. 5.

(2, 3)

Find the midpoint. 6.

(1.5, 4)

Given the midpt and one endpt, find the other endpt.

7. Midpt (3, -6)

Endpt (7, -3) (-1, -9)

Given the midpt and one endpt, find the other endpt.

8. Midpt (-1, 2)

Endpt (3, 0) (-5, 4)

Given the midpt and one endpt, find the other endpt.

9. Midpt (-4, 6)

Endpt (2, 1) (-10, 11)