What are the values for a and b ?

Question

Two points P(a, 13) and Q(- 9, b) are connected by the line segment P Q. the midpoint of segment Q is at (1.5, 3.5) , determine the values for a and b.

Answer 1

(a-9)/2 = 1.5

a/2 = 1.5 + 4.5 = 6

a = 2(6) = 12

(13+b)/2 = 3.5

13/2 + b/2 = 3.5

b/2 = 3.5 - 6.5 = -3

b = (-3)(2) = -6

Answer 2

Use the midpoint formula. x_m = (x₁ + x₂)/2 and y_m = (y₁ + y₂)/2 to get:

1) (a + -9)/2 = 1.5 and

2) (13 + b)/2 = 3.5

Multiplying both sides of equation 1) by 2 it becomes: a - 9 = 3 which is simple to solve.

Multiplying both sides of equation 2) by 2 it becomes: 13 + b = 7 which is also simple to solve.