Question

Find the length of the hypotenuse of the right triangle formed by joining the given points.
$A(-4,4),B(-4,-5),C(7,-5)$

• A. $\sqrt{102}$ units
• B. $\sqrt{202}$ units
• C. $\sqrt{84}$ units
• D. $\sqrt{164}$ units

Answer 1

The correct option is B $\sqrt{202}$ units

The points are $A(-4,4),B(-4,-5),$ and $C(7,-5).$
The image shown below represents the triangle formed by joining the given points.



The hypotenuse of the given triangle is $AC.$

We know:
The length of the side $AC=$ Distance between the points $A$ and $C$

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 $A(-4,4),$ and $C(7,-5)$
$=\sqrt{(-5-4{)}^2+(7-(-4){)}^2}$
$=\sqrt{(-9{)}^2+(7+4{)}^2}$
$=\sqrt{(-9{)}^2+(11{)}^2}$
$=\sqrt{81+121}$
$=202$ units

$\Rightarrow$ Option D is correct.