Question

Which of the following represent the length of a diagonal of this trapezoid?

A
B
C
D

Answer 1

Answer:

$\sqrt{\left(a+b\right)^{2}+c^{2}}$

Step-by-step explanation:

The distance between the line joining points A (-b, c) and C (a, o) will be the length of the diagonal of given trapezoid.

Now, $x_{1} = - b,\ y_{1} = c\ and\ x_{2} = a, y_{2} = 0$

Now, using distance formula,

AC = $\sqrt{\left (x_{2}-x_{1}\right )^{2}+\left (y_{2}-y_{1}\right )^{2}}$

AC = $\sqrt{\left(a-(-b) \right)^{2}+\left(0-c\right)^{2}}$

AC = $\sqrt{\left(a+b\right)^{2}+\left(-c\right)^{2}}$

AC = $\sqrt{\left(a+b\right)^{2}+c^{2}}$

Therefore, the length of diagonal AC of trapezoid = $\sqrt{\left(a+b\right)^{2}+c^{2}}$

So, option (4) is the right option.