Question

Find the distance between the points
(i) P(-6, 7) and Q(-1, -5)
(ii) R(a + b, a - b) and S(a - b, - a - b)

Answer 1

(i) Here, $x_1$ = -6, $y_1$ = 7 and $x_2$ = -1, $y_1$ = -5
$\therefore$ PQ = $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$
$\Rightarrow$PQ = $\sqrt{(-1+6{)}^2+(-5-7{)}^2}$ $\Rightarrow$PQ = $\sqrt{\left(25\right)+\left(144\right)}$ = $\sqrt{169}$ = 13
(ii) We have,
RS = $\sqrt{(a-b-a-b{)}^2+(-a-b-a+b{)}^2}$ $\Rightarrow$ $\sqrt{4b^2+4a^2}$
= 2$\sqrt{(a{)}^2+(b{)}^2}$