Question

If quadrilateral ABCD is a rectangle, where A(-5, -5), B(-10, -3), C(-6, 7) and D(x, y) is unknown. Find the coordinates of the fourth vertex Point D. Write your answer as an ordered pair.

Answer choices
(-1,5)

(-5,6)

(5,1)

(-10.-6)

Answer 1

The coordinates of the fourth vertex D of the rectangle ABCD are (-6, 12).

Step-by-step explanation:

To find the coordinates of the fourth vertex point D, we need to use the properties of a rectangle. Since opposite sides of a rectangle are equal in length and parallel, we can use this information to find the coordinates.

The length of side AB is 5 units, and the length of side BC is 10 units. Since side AB is horizontal, the x-coordinate of D must be the same as the x-coordinate of C. Thus, x = -6.

The length of side AD is 5 units, and the length of side CD is 10 units. Since side CD is vertical, the y-coordinate of D must be the same as the y-coordinate of C plus the length of side AD. Thus, y = 7 + 5 = 12.

Therefore, the coordinates of point D are (-6, 12).