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

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Presentation transcript:

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

midpoint of a segment:. a point that divides the midpoint of a segment: a point that divides the segment into two equal halves (point right in the middle of the segment) 10 ft. 10 ft. “P” is the midpoint. P

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

Steps for Finding Midpoint Y X

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

We are going to find the average of the x & y coordinates using…… (-4,2) (4,2) X

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

2. Plug “x” & “y” values into the Midpoint Formula: (-4,2) (4,2) X (x1,y1) (x2,y2) So….x1=-4 y1=2 x2=4 y2=2

Plug the numbers into the formula: x1=-4 y1=2 x2=4 y2=2

Plug the numbers into the formula: x1=-4 y1=2 x2=4 y2=2

Plug the numbers into the formula: x1=-4 y1=2 x2=4 y2=2

Plug the numbers into the formula: x1=-4 y1=2 x2=4 y2=2

3. Simplify. = =

The coordinates of the midpoint are:

Plot the calculated midpoint….was this what you guessed earlier? X This is the midpoint!!!

Calculate the midpoint of the segment. (2,3) X (12,-7)

Plug the values into equation. (x1,y1) (x2,y2). (2,3) (12,-7) Plug the values into equation.

(x1,y1) (x2,y2). (2,3) (12,-7) Simplify.

(x1,y1) (x2,y2). (2,3) (12,-7) Simplify.

Plot the calculated midpoint. Y (2,3) X (12,-7)

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