Answer: Length of diagonal from point (-b,c) to (a,0) is [tex]\sqrt{(a+b)^2+c^2}[/tex]
Length of diagonal from point (b,c) to (-a,0) is [tex]\sqrt{(a+b)^2+c^2}[/tex]
Step-by-step explanation:
The distance formula to find the distance between points (x,y) and (p,q) is given by :-
[tex]d=\sqrt{(x-p)^2+(y-q)^2}[/tex]
The length of diagonal from point (-b,c) to (a,0) is given by :-
[tex]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}[/tex]
The length of diagonal from point (b,c) to (-a,0) is given by :-
[tex]d=\sqrt{(b-(-a))^2+(c-0)^2}\\\\\Rightarrow\ d=\sqrt{(a+b)^2+c^2}[/tex]
Hence, the lengths of the diagonals of the given trapezoid is same as = [tex]\sqrt{(a+b)^2+c^2}[/tex]
