Geometry 2.5 Midpoints

Midpoint for number lines A B The midpoint for AB is found by adding a and b then dividing by 2 A + b 2

Midpoint for number lines 6 10 The midpoint for AB is found by adding a and b then dividing by 2 6 + 10 2

Midpoint for number lines -2 4 The midpoint for AB is found by adding a and b then dividing by 2 -2 + 4 2

What if it’s not a flat line? That’s why we just Learned about The coordinate plane B

What if it’s not a flat line? (x,y) A We just need the X and y coordinates For each end (x,y) B

That is kind of confusing (x1,y1) (x,y) A We have Two points So let’s change How we label them (x2,y2) (x,y) B

Here is your formula ( , ) X1 + X2 2 Y1 + Y2 2

If this is easier for you ( , ) Add X’s 2 Add Y’s 2

(1,8) ( , ) 8 12 2 2 A (4, 6) ( , ) X1 + X2 Y1 + Y2 2 2 1 + 7 8 + 4 (7,4) B ( , )

(-3,6) ( , ) 2 -4 2 2 A (1, -2) ( , ) X1 + X2 Y1 + Y2 2 2 -3 + 5 6 + -10 2 2 (5,-10) B ( , )

MIDPOINT Y1 + Y2 X1 + X2 2 2 (x1,y1) First, We are finding The middle of the X’s Then We are finding The middle of the Y’s And that gives us the MIDPOINT (x2,y2) B

2.5 5-40 (x3 & x5)

x3 & x5 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18