Which of the following represents the length of a diagonal of a trapezoid with vertices of (-b,c), (b,c), (-a,0), and (a,0)?
1- sq root (a+b)^2-c^2
2- sq root (a-b)^2 - c^2
3- sq root (a-b)^2 +c^2
4- sq root (a+b)^2 +c^2
1.D
2.C
3.A
4.C
5.B
6.D
100% correct you can trust me
Draw a diagram. The answer is clearly (4)
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To find the length of a diagonal of a trapezoid with the given vertices, we can use the distance formula.
The distance formula between two points (x1, y1) and (x2, y2) is given by:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's apply the distance formula to find the length of the diagonal for the given trapezoid:
1. The first vertex is (-b, c), and the second vertex is (b, c).
The distance between these two points is sqrt((b - (-b))^2 + (c - c)^2) = sqrt((2b)^2 + 0^2) = sqrt(4b^2) = 2|b|.
2. The third vertex is (-a, 0), and the fourth vertex is (a, 0).
The distance between these two points is sqrt((a - (-a))^2 + (0 - 0)^2) = sqrt((2a)^2 + 0^2) = sqrt(4a^2) = 2|a|.
The length of the diagonal between these two sets of vertices is the sum of these two distances, so it is:
length = 2|b| + 2|a| = 2(|a| + |b|)
Now let's compare the given answer choices with the derived expression:
1 - sqrt((a+b)^2 - c^2)
2 - sqrt((a-b)^2 - c^2)
3 - sqrt((a-b)^2 + c^2)
4 - sqrt((a+b)^2 + c^2)
By comparing the derived expression 2(|a| + |b|) with the given answer choices, we can see that none of the options matches the derived expression. Therefore, none of the provided answer choices represents the correct length of the diagonal of the trapezoid with the given vertices.