Question

Find the length of the base of triangle ABC formed by joining the given points.
$A(-5,-3),B(4,-3),C(-5,4)$.

• A. $6$ units
• B. $8$ units
• C. $9$ units
• D. $4$ units

Answer 1

The correct option is C $9$ units

The points are $A(-5,-3),B(4,-3),$ and $C(-5,4).$
The image shown below represents the triangle formed by joining the given points.



The base of the given triangle is $AB.$

We know:
The length of side $AB=$ Distance between the points $A$ and $B$

As per the distance formula, the distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by
$\sqrt{(y_2-y_1{)}^2+(x_2-x_1{)}^2}$.

So, the distance between the points $(-5,-3)$ and $B(4,-3)$
$=\sqrt{(-3-(-3){)}^2+(4-(-5){)}^2}$
$=\sqrt{(-3+3{)}^2+(4+5{)}^2}$
$=\sqrt{(0{)}^2+(9{)}^2}$
$=\sqrt{0+81}$
$=\sqrt{81}$
$=9$ units

$\Rightarrow$ Option C is correct.