Question

Find all the points that are on the x-axis that are a distance of 13 units from the point (12,-5).

Answer 1

Let point A(x,y) be the point on the x-axis. All points that lie on the x-axis have y-coordinate equal to 0, then A(x,y).

Find the distance from point A to point (12,-5):

$d=\sqrt{(x-12)^2+(0-(-5))^2}=\sqrt{(x-12)^2+25}.$

This distance is equal to 13, then

$\sqrt{(x-12)^2+25}=13,\\ \\(x-12)^2=169-25,\\ \\(x-12)^2=144,\\ \\x-12=12 \text{ or } x-12=-12,\\ \\ x=24 \text{ or }x=0.$

You get two ponts (0,0) and (24,0).