Question

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

Answer 1

Answer:

$H = (5,1)$

Step-by-step 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

$D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

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

$D = \sqrt{(x_2 - x)^2 + (y_2 - y)^2}$ and

$D = \sqrt{(x_1 - x)^2 + (y_1 - y)^2}$

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 $D = \sqrt{(x_2 - x)^2 + (y_2 - y)^2}$

$D = \sqrt{(x_2 - 3)^2 + (y_2 - 2)^2}$

Square both sides:

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

Substitute values for x , y , x1 and y1 in $D = \sqrt{(x_1 - x)^2 + (y_1 - y)^2}$

$D = \sqrt{(4 - 3)^2 + (4 - 2)^2}$

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:

$H = (5,1)$