Question

A construction project requires a surveyor to lay out a structure in the shape of quadrilateral QUAD represented by the vertices Q(9, 2), U(5, 10), A(15, 10), and D(x, y) on a coordinate grid. Determine the coordinates of point D so that the structure is a trapezoid where UA¯¯¯¯¯⊥AD¯¯¯¯¯

.




(5, 2)


(15, 0)


(15, 2)


(13, 14)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine the coordinates of point D, we know that the line UA must be perpendicular to the line AD. This means that the slope of UA multiplied by the slope of AD must equal -1.

The slope of UA is found by finding the change in y divided by the change in x:
slope of UA = (10 - 10) / (5 - 15) = 0

The slope of AD is found by using points A and D:
slope of AD = (y - 10) / (x - 15)

Since the slopes are perpendicular, the product must be -1:
0 * (y - 10) / (x - 15) = -1
0 = -(y - 10) / (x - 15)
0 = -(y - 10)
0 = -y + 10
y = 10

Therefore, the coordinates of point D are (15, 10).

So, the correct answer is:
(15, 10)