Answer to Question #29421 in Analytic Geometry for darcy

Question

find the values a and b if (a,2) is the midpoint of (3,b) and (-5,6)

Answer 1

If (a,2) is the midpoint of (3,b) and (-5,6) then

a = (3 + (-5))/2 (1)
2 = (b + 6)/2 (2)

Let's solve the obtained equations:

(1) ==> a = (3 - 5)/2 = -2/2 = -1;
(2) ==> b + 6 = 2*2 ==> b + 6 = 4 ==> b = 4-6 = -2.

So, a = -1 and b = -2.
Answer: a=-1, b=-2