1. Do now
Write your comparison on the Do Now Sheet.

2. Section 1.3-Use midpoint and distance formulas
Geometry

3. Vocabulary
Segment bisector: a point, ray, line, line segment, or plane that intersects the segment at its midpoint
Midpoint: point that divides the segment into two congruent segments

4. Example 1
In the skateboard design, VW bisects XY at point T, and XT = 39.9 cm. Find XY.
Skateboard
Point T is the midpoint of XY . So, XT = TY = 39.9 cm.
XY = XT + TY =
= 79.8 cm

5. Point M is the midpoint of VW . Find the length of VM .
Example 2
Point M is the midpoint of VW . Find the length of VM .
STEP 1: Write and solve an equation. Use the fact that VM = MW.
STEP 2: Evaluate the expression for VM when x = 4.
VM = 4x – 1 = 4(4) – 1 = 15
VM = MW
4x – 1 = 3x + 3
So, the length of VM is 15.
x – 1 = 3
*** Do a mental check for MW.
x = 4

6. The midpoint formula
If 𝐴 𝑥 1 , 𝑦 1 and B 𝑥 2 , 𝑦 2 are points in a coordinate plane, then the midpoint M of 𝐴𝐵 has coordinates 𝑥 1 + 𝑥 2 2 , 𝑦 1 + 𝑦

7. Example 3 (a) The coordinates of the midpoint M are 𝟓 𝟐 ,− 𝟏 𝟐 .
a. FIND MIDPOINT The endpoints of RS are R(1,–3) and S(4, 2). Find the coordinates of the midpoint M. 2 5
1 + 4
– 3 + 2 = , M – 1
The coordinates of the midpoint M are 𝟓 𝟐 ,− 𝟏 𝟐 .

8. Example 3 (b) STEP 1 Find x. STEP 2 Find y. 1+ x 2 = 4+ y 1 2 =
b. FIND ENDPOINT The midpoint of JK is M(2, 1). One endpoint is J(1, 4). Find the coordinates of endpoint K.
STEP 1
Find x.
STEP 2
Find y.
1+ x 2 =
4+ y 1 2 =
1 + x = 4
4 + y = 2
x = 3
y = – 2
The coordinates of endpoint K are (3, – 2).

9. The distance formula
If 𝐴 𝑥 1 , 𝑦 1 and 𝐵 𝑥 2 , 𝑦 2 are points in a coordinate plane, then the distance between A and B is 𝐴𝐵= 𝑥 2 − 𝑥 𝑦 2 − 𝑦

10. Example 4-Standardized test prep
Use the distance formula

11. Example 4 continued 𝑅𝑆= 𝑥 2 − 𝑥 1 2 + 𝑦 2 − 𝑦 1 2 = 4−2 2 + −1−3 2
𝑅𝑆= 𝑥 2 − 𝑥 𝑦 2 − 𝑦 1 2
= 4− −1−3 2
= (−4) 2
= 4+16
= 20 ≈4.47
The correct answer is C.

12. Homework
Textbook pages 19-20
# 5, 9, 12, 20, 23, 25, 32, 34