Graphing Question

Question

I need to find all points on the x-axis that are 16 units from the point (6,-8). I’m not sure what formula to use to get an ordered pair.

Answer 1

Start with the distance formula.

d = √[(x₁ - x₂)² + (y₁ - y₂)²]

d = 16

Let (x₁,y₁) be a point on the x-axis. Then

x₁ = x = ?

y₁ = 0

Let (x₂,y₂) be (6,-8). Then

x₂ = 6

y₂ = -8

The distance equation becomes

16 = √[(x - 6)² + 64]

Square both sides of this equation and get a quadratic equation in x. Put it in standard form and then solve for x using the quadratic formula. You may end up with two solutions for x. In each case, the point you seek is (x,0). Try to finish from here.