Two different points

Question

Two different points on the line y=2 are each exactly 13 units from the point (7,14). Draw a picture of this situation, then find the coordinates of these points. 

Answer 1

The coordinates of the points are (x,2). Use the distance formula.

(x - 7)² + (2 - 14)² = 13²

(x - 7)² + 144 = 169

(x - 7)² - 25 = 0

x² - 14x + 49 - 25 = 0

x² - 14x + 24 = 0

(x - 2)(x - 12) = 0

x = 2 or 12

The 2 points are (2,2) and (12,2).