find the lengths of the diagonals of this trapezoid (-b, c) (b, c) (-a, 0) (a, 0) x
To find the lengths of the diagonals of the trapezoid, we need to calculate the distances between pairs of vertices.
Let's start by finding the length of the diagonal connecting (-b, c) to (a, 0).
Using the distance formula, the length of this diagonal is given by:
d1 = sqrt((a - (-b))^2 + (0 - c)^2)
= sqrt((a + b)^2 + c^2)
Next, let's find the length of the diagonal connecting (-a, 0) to (b, c).
Using the distance formula again, the length of this diagonal is given by:
d2 = sqrt((b - (-a))^2 + (c - 0)^2)
= sqrt((a + b)^2 + c^2)
Therefore, the lengths of the two diagonals are both sqrt((a + b)^2 + c^2).