Find the lengths of the diagonals of this trapezoid.

trapezoid on a graph with points
(-a,0), (-b,c), (b,c), (a,0)

negative a and b are on the left side (a is on bottom and b is on top) and positive a and b are on the right side (a is on bottom and b is on top)

please please help me :(

http://www.jiskha.com/display.cgi?id=1326887669

To find the lengths of the diagonals of the trapezoid, we can use the distance formula to find the lengths of the sides.

Let's label the points as follows:
(-a,0) as point A
(-b,c) as point B
(b,c) as point C
(a,0) as point D

Now we can find the lengths of the diagonals AD and BC.

To find the length of diagonal AD:
1. Determine the coordinates of points A and D.
A = (-a, 0)
D = (a, 0)

2. Apply the distance formula:
Distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

For diagonal AD:
dAD = sqrt((a - (-a))^2 + (0 - 0)^2)
= sqrt((2a)^2 + 0^2)
= sqrt(4a^2)
= 2a

Therefore, the length of diagonal AD is 2a.

To find the length of diagonal BC:
1. Determine the coordinates of points B and C.
B = (-b, c)
C = (b, c)

2. Apply the distance formula:
For diagonal BC:
dBC = sqrt((b - (-b))^2 + (c - c)^2)
= sqrt((2b)^2)
= sqrt(4b^2)
= 2b

Therefore, the length of diagonal BC is 2b.

In summary,
Length of diagonal AD = 2a
Length of diagonal BC = 2b

To find the lengths of the diagonals of the trapezoid, we can use the distance formula from Analytic Geometry. The distance formula calculates the distance between two points in a Cartesian plane.

Let's start with the first diagonal, which connects the points (-a, 0) and (b, c).
- The horizontal distance between these two points is b - (-a), which simplifies to b + a.
- The vertical distance between these two points is c - 0, which simplifies to c.
- Using the Pythagorean theorem, the length of this diagonal can be calculated using the formula: √((b + a)^2 + c^2).

Now, let's move on to the second diagonal, which connects the points (-b, c) and (a, 0).
- The horizontal distance between these two points is a - (-b), which simplifies to a + b.
- The vertical distance between these two points is 0 - c, which simplifies to -c.
- Again using the Pythagorean theorem, the length of this diagonal can be calculated using the formula: √((a + b)^2 + (-c)^2).

To summarize, the lengths of the diagonals of the trapezoid are:
1. First diagonal: √((b + a)^2 + c^2)
2. Second diagonal: √((a + b)^2 + (-c)^2)

Plug in the values of a, b, and c to calculate the lengths of the diagonals.