Question

HELP ASAP!! A merry-go-round is to be built in a park. The center of the structure is required to be equidistant from three support columns located at Q(4,−2), R(2,−4), and S(0,2). What are the coordinates for the location of the center of the merry-go-round?

Answer 1

Answer:

( 1 , -1)

Step-by-step explanation:

A merry-go-round is to be built in a park. The center of the structure is required to be equidistant from three support columns located at Q(4,−2), R(2,−4), and S(0,2).

Let say coordinates for the location of the center of the merry-go-round = (x , y)

Distance of this point from Q , R & S will be equal

(x - 4)² + (y +2)²  = (x - 2)² + (y + 4)²  =  (x - 0)² + (y - 2)²

Equating 1 st & 3rd first

x² + 16 - 8x + y² + 4 + 4y = x² + y² + 4 - 4y

=> 8y - 8x + 16 = 0

=> y - x + 2 = 0

=> x = y + 2

Equating 2nd & 3rd

x² + 4 - 4x + y² + 16 + 8y = x² + y² + 4 - 4y

=> 12y - 4x + 16 = 0

=> 3y - x + 4 = 0

=> x = 3y + 4

Equating x from both

3y + 4 = y + 2

=> 2y = -2

=> y = -1

x = - 1 + 2 = 1

( 1 , -1) are the coordinates for the location of the center of the merry-go-round

Answer 2

Answer:

The answer is (1, -1)

Step-by-step explanation:

Sorry for answering so late, but I was still able to get points from this answer, so I decided to do it.