Find all points on the xaxis 5 units away from the point 4 3

Find all points on the x-axis 5 units away from the point (4, 3).

Solution

Let the point on x axis be (x, 0)

distance between (x, 0) and (4, -3)

sqrt[ (x-4)^2 +3^2] = 5

(x-4)^2 +9 = 25

(x-4)^2 = 16

taking square root on both sides:

x-4 = +/-4

x = 0 , x= 8

Points are : (0,0) and ( 8, 0)