Th distance between (a+2,4) and (2a, a+7) is 5. Find both values of a that make this true

Question

How to solve this problem

Answer 1

Distance=sqrt((a+3)^2+(a-2)^2)=5.

a^2+6a+9+a^2-4a+4=25; 2a^2+2a-12=0; a^2+a-6=0=(a+3)(a-2); a=-3 or 2. (The two points are (-1,4) and (-6,4); or (4,4) and (4,9). The first pair form a line parallel to the x axis, and the second pair form a line parallel to the y axis.)

Answer 2

-3 and 2