Midpoint by LisaB1982

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```									Midpoint Conjecture
Objectives: Discover formula for finding the midpoint of a segment.

midpoint of a segment: a point that divides the segment into two equal halves (point right in the middle of the segment)
“P” is the midpoint.

You can calculate the midpoint on a coordinate plane as long as you know the coordinates of the endpoints!

Look at this segment…..can you guess the coordinates of the midpoint?

You will now learn the Midpoint Formula…remember your guess (above).

Steps for Finding Midpoint

1. Label the endpoints as (x1,y1) and (x2,y2). (-4,2) (4,2)

(x1,y1)

(x2,y2)

So….x1=-4 x2=4

y1=2 y2=2

We are going to find the average of the x & y coordinates using……

(-4,2)

(4,2)

The Midpoint Formula

…where (x1,y1) & (x2,y2) are coordinates of endpoint of segment.

( x1  x 2) ( y1  y 2) , 2 2

2. Plug “x” & “y” values into the Midpoint Formula: (-4,2) (4,2)

(x1,y1)

(x2,y2)

So….x1=-4 x2=4

y1=2 y2=2

Plug the numbers into the formula:
( x1  x 2) ( y1  y 2) , 2 2

x1=-4 y1=2 x2=4 y2=2

Plug the numbers into the formula:
(4  x 2) ( y1  y 2) , 2 2

x1=-4 y1=2 x2=4 y2=2

Plug the numbers into the formula:

(4  4) ( y1  y 2) , 2 2
x1=-4 y1=2 x2=4 y2=2

Plug the numbers into the formula:

(4  4) (2  2) , 2 2
x1=-4 y1=2 x2=4 y2=2

3. Simplify.

(4  4) (2  2) , 2 2

=

0 4 , 2 2

=

(0,2)

The coordinates of the midpoint are:

(0,2)

Plot the calculated midpoint….was this what you guessed earlier? (0,2)

This is the midpoint!!!

Calculate the midpoint of the segment.
(2,3)

(12,-7)

(x1,y1) (2,3)

(x2,y2). (12,-7)

( x1  x 2) ( y1  y 2) , 2 2
Plug the values into equation.

(x1,y1) (2,3)

(x2,y2). (12,-7)

(2  12) (3  7) , 2 2
Simplify.

(x1,y1) (2,3)
(14) (4) , 2 2

(x2,y2). (12,-7)

(7,2)

Simplify.

Plot the calculated midpoint.

(7,2)
(2,3)

(12,-7)

Calculate the midpoint of the segment that has endpoints at (-17,8) and (-1,11).

(9,1.5)

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