Question
Find the distance between the points $(a ,b)$ and $(-a,-b)$.
✓
Answer
Distance between two points $\left( x _1, y _1\right)$ and $\left( x _2, y _2\right)$
$=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$
$=\sqrt{(a+a)^2+(b+b)^2}$
$=\sqrt{(2 a)^2+(2 b)^2}$
$=\sqrt{4 a^2+4 b^2}$
$=\sqrt{4\left(a^2+b^2\right)}$
$=2 \sqrt{a^2+b^2}$
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