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absor201

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)

Step-by-step 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

[tex]m\:=\:\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]

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)

[tex]m\:=\:\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]

[tex]\left(3,\:2\right)\:=\:\left(\frac{x_2+4}{2},\:\:\frac{y_2+4}{2}\right)[/tex]

so

[tex]\:\:3\:=\:\frac{x_2+4}{2}[/tex]

[tex]x_2+4=6[/tex]

subtract 4 from both sides

[tex]x_2+4-4=6-4[/tex]

[tex]x_2=2[/tex]

and

[tex]2=\:\frac{y_2+4}{2}[/tex]

[tex]\:y_2+4\:=\:4[/tex]

subtract 4 from both sides

[tex]y_2=0[/tex]

Thus, the coordinates of H are:

  • (x₂, y₂) = (2, 0)

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

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