Question

If the point A (0, 2) is equidistant from the points B (3, p) and C (p, 5) the length of AB.

Answer 1

Length of AB = √10 units

Step-by-step explanation:

Given AB = AC. A(0,2), B(3,p) and C (p,5)

AB² = (0-3)² + (2-p)²

= 9 + p² + 4 - 4p

= p² -4p + 13 --------(1)

AC² = (0-p)² + (2-5)²

= p² + 9 --------------(2)

Since (1) = (2), we get:

 p² + 13 - 4p = p² + 9

4p = 4

Therefore p = +1

AB² = p² -4p + 13 = (1)² -4(+1) + 13 = 1 -4 + 13 = 10.

Length of AB = √10 units