Question

If K = (2, 5) and M = (x, −7) and length of KM = 13 units, find the value of x.

Answer 1

Given:

K = (2, 5) 

M = (x, −7) 

Length of KM = 13 units

Use the distance formula to express KM in terms of (x):

\[KM = \sqrt{(x − 2)^2 + (−7 − 5)^2}\]

Simplify the expression inside the square root

\[KM = \sqrt{(x - 2)^2 + (-12)^2} = \sqrt{(x-2)^2 + 144}\]

Given length of KM = 13, square both sides

13² = (x − 2)² + 144

169 = (x − 2)² + 144

Subtract 144 from both sides

169 − 144 = (x − 2)²

25 = (x − 2)²

x − 2 = ±5

x = 2 + 5 = 7 or x = 2 − 5 = −3

x = 7  or x = −3