Question

Find the length of the diagonal AD in the pentagon ABCDE shown in the coordinate plane.

Answer 1

Answer:

$\sqrt{73}$ units.

Therefore, Option C is correct.

Step-by-step explanation:

We have given a pentagon ABCDE

We need to calculate its length

That means we have to find the distance of AD

So, coordinates of A(1,6) and D(4,-2)

Using distance formula:

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Here,$x_1=1,y_1=6,x_2=4,y_2=-2$

On substituting the values we will get:

$\sqrt{(4-1)^2+(-2-6)^2}$

On simplification:

$\sqrt{3^2+(-8)^2}$

$\sqrt{9+64}$

$\sqrt{73}$.

Hence, the length of AD is  $\sqrt{73}$ units.

Therefore, Option C is correct.