Question

Simon wants to create a rectangle on the given coordinate plane. For the left side of the rectangle, he placed his first point at (2, 3), and he placed his second point at (2, 7). After placing the remaining points, he determined the perimeter of the rectangle to be 12 units.
Locate the other two vertices of the rectangle on the coordinate plane.

Answer 1

The other two vertices are (4, 3) and (4, 7).

Explanation:

Step 1:

One point of the rectangle is at (2, 3) and another is at (2, 7).

Since there is a difference only in the y values, this side of the rectangle represents the width of the rectangle.

The width of the rectangle = diference in y values = 7 - 3 = 4 units.

Step 2:

The rectangle has a perimeter of 12 units. The perimeter of any given rectangle is twice the sum of the length and the width of the same rectangle.

Assume the rectangle's length to be x units.

The Perimeter = 2 × (length of the rectange + width of the rectangle)

The Perimeter = $2 (x + 4) = 12$ units.

So the rectangle's length = 2 units.

Step 3:

As we have the two left points of the rectangle, we will get the right vertices by adding the values of x to the two given vertices.

The new vertices = (2+2, 3) and (2+2, 7) = (4, 3) and (4, 7).