Question

Find the lengths of the diagonals of this trapezoid. (image attached)thank you ! :)

Answer 1

Given:

There are given that the trapezoid with vertices:

Explanation:

To find the length of the diagonals, we need to use the distance formula:

So,

From the distance formula:

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

Now,

The length of diagonal from point (-b, c) to (a, 0):

So,

Using the distance formula:

Then,

$\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt{(a+b)^2+(0-c)^2} \\ d=\sqrt{(a+b)^2+c^2} \end{gathered}$

And,

The length of diagonal from point (b, c) to (-a, 0) is given by:

$\begin{gathered} d=\sqrt{(-a-b)^2+(0-c)^2} \\ d=\sqrt{(a+b)^2+c^2} \end{gathered}$

Final answer:

Hence, the distance of the given trapezoid is the same for both the diagonal.

$d=\sqrt{(a+b)^2+c^2}$