In this exercise we use the Distance Formula and the Midpoint Formula. 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

In this exercise we use the Distance Formula and the Midpoint Formula.

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

Answer:

(x,y) = (?,?)

Answer 1

(x1+x2)/2 = Midpoint of x

(y1+y2)/2 = Midpoint of y

Plugging in the values you know:

(-5+x)/2=7 Multiply both sides by 2

2(-5+x)/2=2(7) Distribute and simplify

-5+x=14 Add 5 to both sides

-5+x+5=14+5 Simplify

x=19

(7+y)/2=9 Multiply both sides by 2

2(7+y)/2=2(9) Distribute and simplify

7+y=18 Subtract 7 from both sides

1+y-7=18-7 Simplify

y=11

(19,11) is the other end