do now: pass out calculators. complete eoc review week # 17. have your homework out ready to check
TRANSCRIPT
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.
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
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