A line intersects y -axis and x -axis at point P and Q , respectively. If R(2, 5) is the mid-point of line segment PQ…

CBSE Class 10 Maths PYQ · Coordinate Geometry · Application · 2 Marks · March 2023 · Standard

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1102 Marks · March 2023 · Standard

A line intersects $y$-axis and $x$-axis at point $P$ and $Q$, respectively. If $R(2, 5)$ is the mid-point of line segment $PQ$, then find the coordinates of $P$ and $Q$.

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Let the coordinates of $P$ and $Q$ be $(0, y)$ and $(x, 0)$ respectively.
$\therefore R(2, 5)$ is the midpoint of $PQ$
$\frac{0+x}{2} = 2$ and $\frac{y+0}{2} = 5$
$\therefore x = 4, y = 10$
$P(0, 10)$ and $Q(4, 0)$