The Distance Formula...The Distance Formula Example Find the distance between (1, 4) and (-2, 3)....

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.

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.

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.

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.

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

• 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

• 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

• 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 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

• What is the length of the altitude of an

equilateral triangle if a side is 12 cm?

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.

x = 10.4 cm

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)

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)

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.

Find the midpoint. 5.

(2, 3)

Find the midpoint. 6.

Find the midpoint. 6.

(1.5, 4)

Given the midpt and one endpt, find the

other endpt. 7.

Midpt (3, -6)

Endpt (7, -3)

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)

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)

Given the midpt and one endpt, find the

other endpt. 9.

Midpt (-4, 6)

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

Partition Line

Segments (1 Dimension)

1 2 1( )

ax x x

a b

Partition – 1 Dimension

P is at 1, and Q is at 7.

Find the point, T, so that T partitions P to Q in a 2:1 ratio.

1 2 1

( )a

x x xa b

Partition – 1 Dimension

C is at -6 and D is at 4.

Find the point, T, so that T is C to D in a 2:3 ratio.

1 2 1

( )a

x x xa b

Partition – 2 Dimension

Given the points A(-2,4) and

B(7,-2), find the coordinates of the

point P on the directed line segment

AB that partitions AB in the ratio

1:2.

1 2 1

( )a

x x xa b