Question

Given that the coordinates of points $A$ and $B$ are $(-3,2)$ and $(9,7)$ respectively, find the following without using squared paper.
(i) Coordinates of mid-point of $AB.$
(ii) Distance between $A$ and $B.$

Answer 1

(i)

By using mid-point formula midpoint $P$(let say) of $A$ and $B$ will be,

$\begin{array}{cc}P& =\left(\frac{-3+9}{2},\frac{2+7}{2}\right)\\ & =\left(\frac{6}{2},\frac{9}{2}\right)\\ & =\left(3,4.5\right)\end{array}$

(ii)

By using the distance formula,

$\begin{array}{cc}AB& =\sqrt{{\left(9+3\right)}^2+{\left(7-2\right)}^2}\\ & =\sqrt{{12}^2+5^2}\\ & =\sqrt{144+15}\\ & =\sqrt{169}\\ & =13\text{units}\end{array}$