Question

given A(a,2) B(3,4) and C(-2,1). if A is at the same distance to the point B and C find a

Answer 1

Use distance formula (point-to-point):
d = sqrt((y2 - y1)^2 + (x2 - x1)^2)
where (x1,y1) and (x2,y2) are the points involved.

In the problem, it was said that the distances from A -> B and A -> C are equal. Therefore,
sqrt((4 - 2)^2 + (3 - a)^2) = sqrt((1 - 2)^2 + (-2 - a)^2)

Squaring both sides to remove the squareroot sign:
(4 - 2)^2 + (3 - a)^2 = (1 - 2)^2 + (-2 - a)^2
(-2)^2 + (3 - a)^2 = (-1)^2 + (-2 - a)^2
4 + 9 - 6a + a^2 = 1 + 4 + 4a + a^2
13 - 6a = 5 + 4a
-6a - 4a = 5 - 13
-10a = -8
a = 4/5

Hope this helps~ `u`

Answer 2

tnx