MATH SOLVE

3 months ago

Q:
# The longer base of an isosceles trapezoid joins points (-3, -2) and (7, -2). One endpoint of the shorter base is (-1, 4). What are the coordinates of the other endpoint?a. (5, 4)b. (4, 5)c. (0, -3)

Accepted Solution

A:

We have:

A(-3, -2)

B(7, -2)

C(-1, 4)

The difference between Xc and Xa will be half the difference between the longer and the shorter base.

Xc- Xa = -1 - (-3) = -1 + 3 = 2

The longer base length is given by

Xb - Xa = 7 - (-3) = 7 + 3 = 10

Therefore the shorter base will be 10 - 2×2 = 6 units long.

Hence, we need to find the point that is 6 units on the right of C, which means:

Xd = Xc + 6 = -1 + 6 = 5

Therefore, the correct answer is A) (5 , 4)

Please, note that you could also reason in a simplier way: you need to find a point that is "at the same height as C", which means that it must have the same y-coordinate. The only option, would be A).

A(-3, -2)

B(7, -2)

C(-1, 4)

The difference between Xc and Xa will be half the difference between the longer and the shorter base.

Xc- Xa = -1 - (-3) = -1 + 3 = 2

The longer base length is given by

Xb - Xa = 7 - (-3) = 7 + 3 = 10

Therefore the shorter base will be 10 - 2×2 = 6 units long.

Hence, we need to find the point that is 6 units on the right of C, which means:

Xd = Xc + 6 = -1 + 6 = 5

Therefore, the correct answer is A) (5 , 4)

Please, note that you could also reason in a simplier way: you need to find a point that is "at the same height as C", which means that it must have the same y-coordinate. The only option, would be A).