Final answer:
The two possible locations of point F, with point G located at (1,4) and a distance of 52 units between them, are found using the distance formula, leading to two possible x-coordinates for F and we get ( 1 ± √2688 ,8) .
Step-by-step explanation:
The distance between two points in a coordinate plane can be found using the distance formula. Since point F is located at (x,8) and point G is at (1,4), and the distance between them is given as 52 units, we need to use the distance formula to find the x-coordinate of point F. The formula is:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the provided details, we get:
52 = √((x - 1)^2 + (8 - 4)^2)
52 = √((x - 1)^2 + 16)
52^2 = (x - 1)^2 + 16
2704 = (x - 1)^2 + 16
(x - 1)^2 = 2688
x - 1 = ±2688
x = 1 ± √2688
Solving for x yields two possible values for x, thus giving us the two potential coordinates for point F as follows:
- F(x, 8) where x = 1 + √2688
- F(x, 8) where x = 1 - √2688