First slide

Cartesian plane

Question

$P$ is a point on $x -$ axis, $Q$ is a point on y-axis. Both are equidistant from the points $(7, 6)$ and $(3, 4)$ . Distance between $P$ and $Q$ is

Moderate

A

$2 \sqrt{5}$
B

$15 \sqrt{5}$
C

$15 \sqrt{5} / 2$
D

$5 \sqrt{15} / 2$

Solution

Let the coordinates of $P$ be $(x, 0)$ and of $Q$ be $(0, y)$ , then
$(x - 7)^{2} + 6^{2} = (x - 3)^{2} + 4^{2} \Rightarrow x = 15 / 2$
and $7^{2} + (y - 6)^{2} = 3^{2} + (y - 4)^{2} \Rightarrow y = 15$
So coordinates of $P$ are $(15 / 2, 0)$ and of $Q$ are $(0, 15)$
$\Rightarrow P Q = \sqrt{{(\frac{15}{2})}^{2} + (15)^{2}} = \frac{15 \sqrt{5}}{2}$

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