If M(7, 9) is the midpoint of the line segment AB and if A has coordinates (−5, 7), find the coordinates of B.

Question

If M(7, 9) is the midpoint of the line segment AB and if A has coordinates (−5, 7),

 find the coordinates of B.

(x,y)= ( , )

Answer 1

Given: M ( 7 , 9 ); A ( -5 , 7 ) ; Solve for B ( X_{2 ,} Y₂ )

( -5 + X₂ ) / 2 = 7

-5 + X₂ = 14

-5 + X₂ + 5 = 14 + 5

X₂ = 19

( 7 + Y₂ ) / 2 = 9

7 + Y₂ = 18

7 + Y₂ - 7 = 18 - 7

Y₂ = 11

The coordinates of B ( 19 , 11 )

Answer 2

(-5 + x) / 2 = 7 ---> -5 +x = 14 --> x = 19

(7 + y)/2 = 9 ---> y+7 = 18 ---> y = 11

(19,11) vs (-5,7) has midpoint (7,9)