Which of the following points is the fourth vertex needed to create a rectangle with vertices located at (-25, 18) and (-13, -9)?

The fourth vertex needed to complete a rectangle with vertices at A(-25, 18) and B(-13, -9) can be one of the following: C (-32.5, -1.5) or D (-5.5, 10.5). These points ensure that all vertices maintain the properties of a rectangle. The coordinates are derived from the midpoint and the necessary perpendicular slopes.
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Answered by Anonymous | 2025-07-05

Step 1: Determine the characteristics of a rectangle
A rectangle has opposite sides that are parallel and equal in length. This means that the x-coordinates of two opposite vertices will be the same, and the y-coordinates of the other two opposite vertices will be the same.
Step 2: Identify the given vertices
Given vertices are (-25, 18) and (-13, -9). Let's find the other two vertices that would form a rectangle with these points.
Step 3: Calculate the differences in x and y coordinates
The difference in x-coordinates between the given points is -13 - (-25) = 12.
The difference in y-coordinates between the given points is -9 - 18 = -27.
Step 4: Determine the fourth vertex
If the given points are (-25, 18) and (-13, -9), the other two points would be (-25, -9) and (-13, 18) to form a rectangle. Let's verify:

The point (-25, -9) would be directly below (-25, 18), and (-13, 18) would be directly to the right of (-25, 18), forming a rectangle with the given points.

Step 5: Identify the fourth vertex needed
Given that one of the points is (-25, 18) and the other is (-13, -9), and if we consider (-25, 18) and (-13, -9) as diagonally opposite vertices of the rectangle, the fourth vertex would be (-13, 18).
The final answer is: ( − 13 , 18 ) ​ ;

Answered by Caesar2050 | 2025-07-05