Coordinate Geometry

Question

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

Solution

Since a line is intersecting Y-axis at P and X- axis at Q,

Coordinates of P = (0,y) and coordinates of Q = (x,0)

Let R be the midpoint of PQ.

$Then, co - ordinates of R = (\frac{0 + x}{2}, \frac{y + 0}{2}) = (2, - 5) \Rightarrow (\frac{x}{2}, \frac{y}{2}) = (2, - 5) \Rightarrow \frac{x}{2} = 2 and \frac{y}{2} = - 5 \Rightarrow x = 4 and y = - 10 Hence, co - ordinates of P are (0, - 10) and co - ordinates of Q are (4, 0) .$

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Coordinate Geometry

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

Some More Questions From Coordinate Geometry Chapter

Prove that the diagonals of a rectangle ABCD, with vertices A(2, -1), B(5, -1), C(5, 6) and D(2, 6), are equal and bisect each other.

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