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¯¯¯¯¯

.




a.(5, 2)


b.(15, 0)


c.(15, 2)


d.(13, 14)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To ensure that UA¯¯¯¯¯⊥AD¯¯¯¯¯, the slope of UA must be the negative reciprocal of the slope of AD.

First, find the slope of UA:
Slope of UA = (10-10)/(5-15) = 0

Since the slope of UA is 0, the negative reciprocal will be undefined.

This means that AD must be a vertical line. The x-coordinate of D must be 15 to be vertically aligned with the x-coordinate of A.

Therefore, the coordinates of point D are (15, y). To determine y, we know that UD must be perpendicular to UA, which is a horizontal line.

Therefore, y = 10

So, the coordinates of point D are (15, 10), which corresponds to answer choice b. (15, 0).