Do Now:

• Pass out calculators. • Complete EOC Review Week # 17. • Have your homework out ready to

check.

Do Now:• Pass out calculators. • Complete the problem below. Write an explanation next

to each multiple choice answer.

Objective:

• To apply the distance and midpoint formulas.

Distance Formula:

EXAMPLE 1 Find the distance between two points

Find the distance between (– 1, 3) and (5, 2)

Let ( x1, y1 ) = ( –1, 3) and ( x2, y2 ) = ( 5, 2 ).

d ( x2 – x1 )2 + ( y2 – y1)2= Distance formula

= (5 – (–1))2 + ( 2 – 3)2 Substitute.

= 62 + (– 1)2 = 37 Simplify.

ANSWER

The distance between the points is units.37

Extra Example…

Find the distance between (-3, 1) and (2, 3).

GUIDED PRACTICE for Examples 1 and 2

Find the distance between the points.1. (3, 0), (3, 6)

ANSWER

The distance between the points is 6 units.

2. (–2, 1), (2, 5)

ANSWER

The distance between the points is 4 units. 2

3. (6, –2), (–4, 7)

ANSWER

The distance between the points is units.181

EXAMPLE 2 Find a missing coordinate

The distance between (3, – 5) and (7, b) is 5 units. Find the value of b.

SOLUTION

Use the distance formula with d = 5. Let ( x1, y1 ) = ( 3, –5) and ( x2, y2 ) = ( 7, b ). Then solve for b

d ( x2 – x1 )2 + ( y2 – y1)2= Distance formula

Substitute.= (7 – 3)2 + ( b – (– 5))25

Multiply.= 16 + b2 + 10b + 255

EXAMPLE 2 Find a missing coordinate

Simplify.= b2 + 10b + 415

Square each side. b2 + 10b + 4125 =

Write in standard form. b2 + 10b + 160 =

Factor. (b + 2)(b + 8)0 =

b + 2 = 0 or b + 8 = 0 Zero-product property

b = – 2 or b = – 8 Solve for b.

ANSWER

The value of b is – 2 or – 8

GUIDED PRACTICE for Examples 1 and 2

4. The distance between (1, a) and (4, 2) is 3 units. Find the value of a.

ANSWER

The value of a is 2.

EXAMPLE 3 Standardized Test Practice

SOLUTION

Let ( x1, y1 ) = ( –1, – 2) and ( x2, y2 ) = ( 3, – 4 ).

( )x1 + x2 y1 + y2

2 2, = ( )

– 1 + 3 – 2 + (– 4) 2 2

, Substitute

= (1,– 3) Simplify

ANSWER

The correct answer is B.

GUIDED PRACTICE for Examples 3 and 4

5. Find the midpoint of the line segment withendpoints (4, 3) and (2, 5).

(3, 4)ANSWER

Pg. 748 # 39, 41

Exit Ticket:

1. Can you find the distance between two points? • Find the distance between (4, 8), (4, 7)

2. Can you find the missing coordinate using the distance formula?

• (13, -3), (b, 2); d = 13

3. Can you find the midpoint of the line segment with the given endpoint?

• (6, -3), (4, -7)