Question

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

Answer 1

Note: It seems, you missed to add the correct option. But, I am solving the question to clear your concept anways.

Answer:

The coordinates of H are:

• (x₂, y₂) = (2, 0)

Explanation:

Given the points

• F(3, 2)

• G(4, 4)

Since Point G and point H are the same distance from point F, therefore the point F is the mid-point of G and H

using the mid-point formula

`m\:=\:\left((x_2+x_1)/(2),\:\:(y_2+y_1)/(2)\right)`

Since the point F is the mid-point of G and H, so

m = (3, 2)

as

• (x₁, y₁) = (4, 4) = G

• (x₂, y₂) = H = ?

Thus, substituting m = (3, 2), (x₁, y₁) = (4, 4) to determine coordinates of the point H (x₂, y₂)

`m\:=\:\left((x_2+x_1)/(2),\:\:(y_2+y_1)/(2)\right)`

`\left(3,\:2\right)\:=\:\left((x_2+4)/(2),\:\:(y_2+4)/(2)\right)`

so

`\:\:3\:=\:(x_2+4)/(2)`

`x_2+4=6`

subtract 4 from both sides

`x_2+4-4=6-4`

`x_2=2`

and

`2=\:(y_2+4)/(2)`

`\:y_2+4\:=\:4`

subtract 4 from both sides

`y_2=0`

Thus, the coordinates of H are:

• (x₂, y₂) = (2, 0)

Note: It seems, you missed to add the correct option.