Question

Find the coordinates of the fourth vertex given the points

(−3,2), (−3,−1), and (3,−1).

a) (3,2)
b) (3,−2)
c) (−3,−2)
d) (−3,1)

Answer 1

The fourth vertex of a rectangle formed by the points (−3,2), (−3,−1), and (3,−1) has the coordinates (3,2), which corresponds to option a).

Step-by-step explanation:

To find the coordinates of the fourth vertex of a rectangle, we can use the properties of rectangles. In this case, the given points are (−3,2), (−3,−1), and (3,−1). We notice that the first two points have the same x-coordinate, which means they are vertical corners of the rectangle. The third point shares the same y-coordinate with the second point, so it is a horizontal corner from the second point.

Therefore, the fourth point must have the same x-coordinate as the third point (since it's directly across from the first point) and the same y-coordinate as the first point (since it's directly across from the second point). Thus, the coordinates for the fourth vertex are (3,2). This corresponds to option a).