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Mathematics

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

Section Formula

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Answer

Let image be B(x, y).

Since, A is reflected in P to become B. So, P is mid-point of AB.

By formula,

Mid-point (M) = (x1+x22,y1+y22)\Big(\dfrac{x1 + x2}{2}, \dfrac{y1 + y2}{2}\Big)

Substituting values we get,

⇒P=(5+x2,−3+y2)⇒(−1,3)=(5+x2,−3+y2)∴−1=5+x2 and 3=−3+y2⇒x+5=−2 and y−3=6⇒x=−7 and y=9.\Rightarrow P = \Big(\dfrac{5 + x}{2}, \dfrac{-3 + y}{2}\Big) \\[1em] \Rightarrow (-1, 3) = \Big(\dfrac{5 + x}{2}, \dfrac{-3 + y}{2}\Big) \\[1em] \therefore -1 = \dfrac{5 + x}{2} \text{ and } 3 = \dfrac{-3 + y}{2} \\[1em] \Rightarrow x + 5 = -2 \text{ and } y - 3 = 6 \\[1em] \Rightarrow x = -7 \text{ and } y = 9.

B = (x, y) = (-7, 9).

Hence, image of the point A(5, -3) under reflection in the point P(-1, 3) is (-7, 9).

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