1.3 – Use Midpoint and Distance Formulas & Segment Constructions

Midpoint: Point in the middle of a segment A M B M is the midpoint of

Point, line, or segment that cuts a segment in half Segment bisector: C A M B A M B pt. M bisects D bisects

Perpendicular: Line that intersects at a right angle C A B D

Perpendicular bisector: Perpendicular Line or segment that bisects a segment C A M B D

1. Find the midpoint of A(2, 5) and B(2, -3).

2. Find the midpoint of A(-3, 4) and B(7, 4).

3. Find the midpoint of A(5, 8) and B(1, 2).

Midpoint Formula: Remember! Your answer should be an ordered pair!

4. Find the midpoint of A(-6, 2)and B(-2, -3). midpt AB =

17cm 17cm DF = 34cm

1 2 16 GJ = in

Find MF. 7x – 6 = 5x MF = 5(3) = 15u – 6 = -2x 3 = x M is the midpoint of the segment. Find the indicated length. Find MF. 7x – 6 = 5x MF = 5(3) = 15u – 6 = -2x 3 = x

Find LN. 11x – 21 = 8x + 15 LN = 11(12)-21 + 8(12)+15 3x – 21 = 15 M is the midpoint of the segment. Find the indicated length. Find LN. 11x – 21 = 8x + 15 LN = 11(12)-21 + 8(12)+15 3x – 21 = 15 = 132 – 21 + 96 +15 3x = 36 = 222u x = 12

Distance: Length of a segment

7. Find AB. A(2, 5) and B(2, -3). AB = 5 – (-3) A = 8 = 8u B

8. Find AB. A(-3, 4) and B(7, 4). AB = 7 – (-3) = 10 A B = 10u

9. Find AB. A(5, 8) and B(1, 2). 42 + 62 = c2 A 16 + 36 = c2 c 6 52 = c2 4 B = c AB = u

Distance Formula: A c 6 4 B

10. Find the midpoint and distance between A(-1, 2)and B(3, 4). midpt AB = A B

10. Find the distance between A(-1, 2)and B(3, 4). (3 – (-1))2 + (4 – 2)2 (4)2 + (2)2 A B 16 + 4 u

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

(-2 – 2)2 + (0 – (-3))2 (-1 – 4)2 + (6 – 3)2 (-4)2 (-5)2 (3)2 + (3)2 + The endpoints of two segments are given. Find each segment length. Tell whether the segments are congruent. (-2 – 2)2 + (0 – (-3))2 (-1 – 4)2 + (6 – 3)2 (-4)2 (-5)2 (3)2 + (3)2 + 16 25 + 9 + 9 Not 