Find all ordered pairs on the x-axis of a cartesian coordinate system that are 5 units from the point (0,4)

Question

coordinate..............

Answer 1

If you draw a circle centered at (0,4) & having radius 5, it will intersect with the x-axis twice.  Do you see two different "3-4-5" right triangles created with one leg length 4, hypotenuse 5?

Answer 2

The distance formula is relevant here.

 

d = √[(x1 - x2)^2 + (y1 - y2)^2]

 

d = 5 (given)

 

(x1, y1) = (0, 4)

 

(x2, y2) = (x2, 0), since we want points on the x-axis, i.e. where y = 0

 

5 = √[(0 - x2)^2 + (4 - 0)^2] = √(x2^2 + 16)

 

Square both sides and get

 

25 = x2^2 + 16

 

x2^2 = 25 - 16 = 9

 

x2 = ±3

 

y2 = 0

 

The ordered pairs are (-3, 0) and (3, 0).