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

Point G and point H are the same distance form point F. Which coordinates could be-example-1
User Eryka
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1 Answer

6 votes

Answer:


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)

User Nuri Akman
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