Question

On the coordinate plane, point F is located at (x, 8) and point G is located at (1, 4). The

distance between points F and G is √ √52 units.
What are the two possible locations of point F?

Answer 1

Explanation:

`a^(2) + b^(2) = c^(2) \\4^(2) +b^(2) = (√(52) )^(2) \\16 + b^(2) = 52\\b^(2) =36\\√(b^2) =√(36) \\b=6\\`

One of the possible x-values of point F will be 6 units to the right of point G. So, the x-value of point F could be 7, since 1+6=7. That means one possible location of point F is (7,8).

The other possible x-value of point F will be 6 units to the left of point G. So, the x-value of point F could be -5, since 1–6=–5. That means the other possible location of point F is (–5,8).

So the answer is:

(7,8) and (-5,8)