# Question #f11e4

Jan 1, 2018

$\textcolor{g r e e n}{A B = 1}$

$\textcolor{b l u e}{A D = 1}$

#### Explanation:

Shortest distance between two points can be calculated, as under, if the coordinates of the two points are given:

Distance $d = \sqrt{{\left({x}_{1} - {x}_{2}\right)}_{2} + {\left({y}_{1} - {y}_{2}\right)}^{2}}$ where
$\left({x}_{1} , {y}_{1}\right) , \left({x}_{2} , {y}_{2}\right)$ are the coordinates of the two points between which the distance is calculated.

Given
Coordinates of $A = \left(- 3 , - 1\right) , B = \left(- 2 , - 1\right) , D = \left(- 3 , - 3\right)$

Distance $A B = \sqrt{{\left(- 3 - \left(- 2\right)\right)}^{2} + {\left(- 1 - \left(- 1\right)\right)}^{2}} = 1$
Since y coordinates are the same, distance $\textcolor{g r e e n}{A B = \left(- 2 - \left(- 3\right)\right) = 1}$

Similarly, Distance $A D = \sqrt{{\left(- 3 \left(- 3\right)\right)}^{2} + {\left(- 1 - \left(- 3\right)\right)}^{2}} = 2$
Since x coordinates are the same, distance $\textcolor{b l u e}{A D = \left(- 1 - \left(- 3\right)\right) = 2}$