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Mathematics

The coordinates of the mid-point of the line segment PQ are (1, -2). The coordinates of P are (-3, 2). Find the coordinates of Q.

Section Formula

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Answer

Let the coordinates of Q be (x, y)

Coordinates of P are (-3, 2) and mid-point of PQ are (1, -2) then by mid-point formula, we get

1=(−3+x)2 and (−2)=(2+y)21 = \dfrac{(-3 + x)}{2} \text{ and } (-2) = \dfrac{(2 + y)}{2}

⇒ -3 + x = 2 and 2 + y = -4
⇒ x = 2 + 3 and y = -4 - 2
⇒ x = 5 and y = -6.

Hence, coordinates of Q are (5, -6).

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