Question

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

A. √ 89 units
B. 5 units
C. √ 73 units
D. √ 41 units

Answer 1

`√(73)` units.

Therefore, Option C is correct.

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:

`√((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:

`√((4-1)^2+(-2-6)^2)`

On simplification:

`√(3^2+(-8)^2)`

`√(9+64)`

`√(73)`.

Hence, the length of AD is
`√(73)` units.

Therefore, Option C is correct.