Question

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

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\green{\underline \bold{Given :}}$

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• Coordinates of mid point of line segment PQ are (1 , -2)

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• Coordinates of P are (-3 , 2)

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$\red{\underline \bold{To \: Find:}}$

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• The coordinates of Q

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$\large{\orange{\underline{\tt{Solution :-}}}}$

Let the coordinates of Q be $\rm (x_2 , y_2)$

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$\underline{\bold{\texttt{By mid point formula:}}}$

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$\purple\longrightarrow$ $\sf (\dfrac { x_1 + x_2 } { 2 } , \dfrac { y_1 + y_2 } { 2 })$

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Where $\sf x_1 \: \& \: y_1$ are coordinates of point P

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$\sf \longmapsto (\dfrac { -3 + x_2 } { 2 } , \dfrac { 2 + y_2 } { 2 })$

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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$\bf \implies \dfrac { -3 + x_2 } { 2 } = 1$

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$\sf \longmapsto x_2 - 3 = 2$

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$\bf\dashrightarrow x_2 = 5$

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Also,

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$\bf \implies \dfrac { 2 + y_2 } { 2 } = -2$

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$\sf \longmapsto y_2 + 2 = -4$

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$\bf \dashrightarrow y_2 = -6$

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

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