1. 5-Minute Check

2. 1.3 Use Midpoints & Distance Formulas
Students will analyze segments and determine lengths in the coordinate plane.
Why? So you can solve real world problems dealing with length, as seen in Ex 1.
Mastery is 80% or better on 5-min checks and indy practice.

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

4. Example 1 Find segments lengths
Find RS
RS= _RT_ + _TS_
Segment Addition Postulate
= _21.7_ + _21.7_
Substitute.
RS = _43.4._
Add.
Solution
Point _T_ is the midpoint of RS. So, RT = _TS_ = 21.7.

5. Guided Practice…..White Boards
Find CB
Find AB
Answer 2 1/4
Answer 4 1/2

6. Quick Write
If B is between AC and collinear is it a midpoint? Explain

7. Example 2 Use algebra with segment lengths
Write and solve an equation.
BC = CD
Write equation.
_3x – 2_ = _2x + 3_
Substitute.
_x – 2_ = _3_
Subtract _2x_ from each side.
x = _5_
Add _2_ to each side.
Step 2
Evaluate the expression for BC when x = _5_
BC = _3x – 2_ = _3(5) – 2_ = _13_
So, the length of BC is _13_.

8. Think….Ink…..Share
Point K is the midpoint of JL . Find the length of JL
8-3x=2x+5
8=5x+5
3=5x
X=3/5……plug in to solve JL = 12 2/5

9. 5-Min Check 1. What does it mean to bisect a segment?
Simply put, it cuts a segment in half.
2. Line l bisects segment AC at point B. If segment AC is 19 cm, what is the measure of BC?
9.5 cm
3. M is the Midpoint of AC. If AM is x+5 and MC is 2x, what is the length of AM? 10

10. THE MIDPOINT FORMULA
The coordinates of the midpoint of a segment are the averages of the x-coordinates and of the y-coordinates of the endpoints.
If A(x1,y1)and B(x2, y2) are points in a coordinate plane, then the midpoint M of AB has coordinates

11. Guided …Example 3 Use the Midpoint Formula
The end points of PR are P(–2, 5) and R(4, 3). Find the coordinates of the midpoint M.
The midpoint of AC is M(3, 4). One endpoint is A(l, 6). Find the coordinates of endpoint C.
X1 X2 Y1 Y2 2 2

12. Midpoints Cont..
The coordinates of the midpoint of PR are
(1,4)

13. Guided….Endpoint Option 1 & 2
The midpoint of XZ is M(5, –6). One endpoint is X(–3, 7). Find the coordinates of endpoint Z
Step 1 Find x.
M = (X1 +X2) Substitute for what we know. 2
Step 2 Find y.
M = (Y1 + Y2) Substitute for what we know.

14. Distance Formula

15. Think…Ink…Share
What is the approximate length of RT, with endpoints R(3, 2) and T(–4, 3)?
Solution
Sq Root of 50 Or
7.07

16. What was the Objective for today?
Students will analyze segments and determine lengths in the coordinate plane.
Why? So you can solve real world problems dealing with length, as seen in Ex 1.
Mastery is 80% or better on 5-min checks and indy practice.

17. Assignment
PDF Online