Question

a rectangle in the coordinate plane has vertices at (5, 6), (9, 2), and (5, 2). what are the coordinates of the fourth vertex? (6, 5) (2, 5) (2, 9) (9, 6)

Explanation:

Step1: Recall rectangle properties

In a rectangle, opposite sides are parallel and equal.

Step2: Analyze x - coordinates

The x - coordinates of the given points are 5 and 9. Since opposite sides have equal lengths in the x - direction, the x - coordinate of the fourth vertex should be the same as the non - repeated x - coordinate among the given points, which is 9.

Step3: Analyze y - coordinates

The y - coordinates of the given points are 6 and 2. Since opposite sides have equal lengths in the y - direction, the y - coordinate of the fourth vertex should be the same as the non - repeated y - coordinate among the given points, which is 6.

Answer:

D. (9, 6)