find all points having an x-coordinate of 4 whose distance from the point (1,5) is 5

Answer 1

Use the distance formula.

Answer 2

which is?

Answer 3

It should be on your formula sheet if not then look it up.

Answer 4

you know that all points at a distance 5 will form a circle with center at (1,5) and radius 5. So,

(x-1)^2 + (y-5)^2 = 25

So, plug in x=4 and you have

3^2 + (y-5)^2 = 25
(y-5)^2 = 16
y-5 = ±4
y = 9 or 1

So, the points are (4,9) and (4,1)

Answer 5

Thanks Steve!