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Mathematics

Find the reflection (image) of the point (5, -3) in the point (-1, 3).

Section Formula

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Answer

Let the coordinates of the image of the point A(5, -3) be A'(x, y) in the point (-1, 3) then,

The point (-1, 3) will be the mid-point of AA'

By midpoint formula,

⇒−1=(5+x)2 and 3=(−3+y)2\Rightarrow -1 = \dfrac{(5 + x)}{2} \text{ and } 3 = \dfrac{(-3 + y)}{2}
⇒ 5 + x = -2 and -3 + y = 6
⇒ x = -2 - 5 and y = 6 + 3
⇒ x = -7 and y = 9.

∴ A' = (x, y) = (-7, 9).

Hence, the coordinates of the images of (5, -3) in the point (-1, 3) is (-7, 9).

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