1.3 – Use Midpoint and Distance Formulas & Segment Constructions

Midpoint: Point in the middle of a segment

A BM

M is the midpoint of AB

MBAM

Segment bisector: Point, line, or segment that cuts a segment in half

A BM

pt. M bisects AB

MBAM

A BM

C

D

bisects ABCD

MBAM

Perpendicular: Line that intersects at a right angle

A B

C

D

CDAB

Perpendicular bisector: Perpendicular Line or segment that bisects a segment

A BM

C

D

CDAB

AM MB

Distance: Length between two points

AB

Measured in units

17cm 17cm

DF = 34cm

1. Line bisects the segment. Find the indicated length.

GJ = 16 12 in

1. Line bisects the segment. Find the indicated length.

2. M is the midpoint of the segment. Find the indicated length.

Find MF.

7x – 6 = 5x– 6 = -2x

3 = x

MF = 5(3) = 15u

2. M is the midpoint of the segment. Find the indicated length.

Find LN.

11x – 21 = 8x + 153x – 21 = 15

3x = 36x = 12

LN = 11(12)-21 + 8(12)+15

= 132 – 21 + 96 +15= 222u

3. Find the midpoint and distance of AB, where A(2, 5) and B(2, -3).

A

B

M

M(2, 1)

A

B

AB = 8u

3. Find the midpoint and distance of AB, where A(2, 5) and B(2, -3).

4. Find the midpoint and distance of AB, where A(-3, 4) and B(7, 4).

A BM M(2, 4)

A B

AB = 10u

4. Find the midpoint and distance of AB, where A(-3, 4) and B(7, 4).

5. Find the midpoint and distance of AB, where A(5, 8) and B(1, 2).

A

B

M M(3, 5)

A

B

5. Find the midpoint and distance of AB, where A(5, 8) and B(1, 2).

4

6

42 + 62 = c2

c16 + 36 = c2

52 = c2

132 = c

AB = 132 u

Midpoint Formula:

2,

22121 yyxx

Remember! Your answer should be an ordered pair!

Distance Formula:

2122

12 yyxxAB

Don’t forget your units!

6. Find the midpoint and distance of AB, where A(-6, 2)and B(-2, -3).

2,

22121 yyxx

1x 2x1y 2y

midpt AB =

14,2

6 2,

2

2 3

2

8,

2

1

2

2122

12 yyxxAB

41 u

(-2 – (-6))2+ (-3 – 2)2

(4)2 + (-5)2

16 + 25

6. Find the midpoint and distance of AB, where A(-6, 2)and B(-2, -3).1x 2x1y 2y

7. Find the midpoint and distance of AB, where A(-1, 2)and B(3, 4).1x 2x1y 2y

2,

22121 yyxx

midpt AB =

3,1

1 3,

2

2 4

2

2,2

6

2

2122

12 yyxxAB

20

52 u

(3 – (-1))2 + (4 – 2)2

(4)2 + (2)2

16 + 4

7. Find the midpoint and distance of AB, where A(-1, 2)and B(3, 4).1x 2x1y 2y

The endpoints of two segments are given. Find each segment length. Tell whether the segments are congruent.

P

Q

R

S

The endpoints of two segments are given. Find each segment length. Tell whether the segments are congruent.

2122

12 yyxxPQ 2122

12 yyxxRS

34 25

5Not

(-1 – 4)2 + (6 – 3)2

(-5)2 + (3)2

25 + 9

(-2 – 2)2 + (0 – (-3))2

(-4)2 + (3)2

16 + 9

HW Problem1.3 19-22 2, 3-21 odd, 24, 33, 37, 43, 57-59

What does the red circle mean around the problem number?

**Bring your protractor tomorrow!

# 15

x + 15 = 4x – 45 15 = 3x – 45 60 = 3x

20 = x

SU = 2(20+15)

SU = 2(35)

SU = 70u