Question

Point G and point H are the same distance form point F. Which coordinates could be the location of point H?

Answer 1

`H = (5,1)`

Explanation:

The attachment is not clear. However, the points of G and F are:

`F = (3, 2)`

`G = (4, 4)`

And the options are:

`A.\ (1, 2) \\ B. (4, 2)\\ C. (5, 1) \\ D. (2, 5)`

Required

Determine the coordinates of H

This question will be solved using distance formula, D

`D = √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

Since F is equidistant of G and H, the formula can be represented as:

`D = √((x_2 - x)^2 + (y_2 - y)^2)` and

`D = √((x_1 - x)^2 + (y_1 - y)^2)`

Where:

`(x_1,y_1) = (4,4)`

`(x,y) = (3,2)`

`H = (x_2,y_2)`

Substitute values for x , y , x2 and y2 in
`D = √((x_2 - x)^2 + (y_2 - y)^2)`

`D = √((x_2 - 3)^2 + (y_2 - 2)^2)`

Square both sides:

`D^2 = (x_2 - 3)^2 + (y_2 - 2)^2`

Substitute values for x , y , x1 and y1 in
`D = √((x_1 - x)^2 + (y_1 - y)^2)`

`D = √((4 - 3)^2 + (4 - 2)^2)`

Square both sides:

`D^2 = (4 - 3)^2 + (4 - 2)^2`

`D^2 = (1)^2 + (2)^2`

`D^2 = 1 + 4`

`D^2 = 5`

Substitute 5 for D^2 in
`D^2 = (x_2 - 3)^2 + (y_2 - 2)^2`

`5 = (x_2 - 3)^2 + (y_2 - 2)^2`

From the list of given options, the values of x and y that satisfy the above condition is: (5,1)

This is shown below

`5 = (5-3)^2 + (1-2)^2`

`5 = (2)^2 + (-1)^2`

`5 = 4 + 1`

`5 = 5`

Other options do not satisfy this condition. Hence, the coordinates of H is:

`H = (5,1)`