The mid-point of a line segment $A B$ is $P (- 3, 3)$ . If $A$ has coordinates $(- 4, 4)$ , then the coordinates of point $B$ are

$(2, - 2)$

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$(- 2, 2)$

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$(- 2, - 1)$

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$(2, - 1)$

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Solution

The correct option is B
$(- 2, 2)$

Let the coordinates of point $B$ be $(x, y)$ .

The mid-point of the line joining two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is given by $(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$

$⟹ (- 3, 3)$ = $(\frac{- 4 + x}{2}, \frac{4 + y}{2})$

$⟹ \frac{- 4 + x}{2} = - 3$ and $\frac{4 + y}{2} = 3$

$⟹ - 4 + x = - 6$ and $4 + y = 6$

$⟹ x = - 2$ and $y = 2$

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