# If points Q and reflections of point P (−3, 4)

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,

$Q R=\sqrt{(3+3)^{2}+(4+4)^{2}}$

$=\sqrt{36+64}$

$=\sqrt{100}$

$=10$