Question:
If points Q and reflections of point P (−3, 4) in X and Y axes respectively, what is QR?
Solution:
We have to find the reflection of (−3, 4) along x-axis and y-axis.
Reflection of any point $P(a, b)$ along $x$-axis is $(a,-b)$
So reflection of $(-3,4)$ along $x$-axis is $Q(-3,-4)$
Similarly, reflection of any point $\mathrm{P}(\mathrm{a}, \mathrm{b})$ along $y$-axis is $(-a, b)$
So, reflection of $(-3,4)$ along $y$-axis is $R(3,4)$
Therefore,
$Q R=\sqrt{(3+3)^{2}+(4+4)^{2}}$
$=\sqrt{36+64}$
$=\sqrt{100}$
$=10$