Question

Find the lengths of the diagonals of this trapezoid.

Answer 1

Answer: Length of diagonal from point (-b,c) to (a,0) is $\sqrt{(a+b)^2+c^2}$

Length of diagonal from point (b,c) to (-a,0) is $\sqrt{(a+b)^2+c^2}$

Step-by-step explanation:

The distance formula to find the distance between points (x,y) and (p,q) is given by :-

$d=\sqrt{(x-p)^2+(y-q)^2}$

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

$d=\sqrt{(-b-a)^2+(c-0)^2}\\\\\Rightarrow\ d=\sqrt{(-1)^2(a+b)^2+c^2}\\\\\Rightarrow\ d=\sqrt{(a+b)^2+c^2}$

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

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

Hence, the lengths of the diagonals of the given trapezoid is same as = $\sqrt{(a+b)^2+c^2}$