Question

Nikki drew a rectangle with a perimeter of 18 units on a coordinate grid. Two of the vertices were (4, –3) and (–1, –3). What could be the coordinates of the other two vertices of the rectangle?

Answer 1

There are two possible solutions for the other two vertices of the rectangle:

(i) (4, 1), (-1, 1), (ii) (4, -7), (-1, -7)

Explanation:

Geometrically speaking, the perimeter of a rectangle (
`p`) is:

`p = 2\cdot b + 2\cdot h` (1)

Where:

`b` - Base of the rectangle.

`h` - Height of the rectangle.

Let suppose that the base of the rectangle is the line segment between (4, -3) and (-1, -3). The length of the base is calculated by Pythagorean Theorem:

`b = \sqrt{[(-1)-4]^(2)+[(-3)-(-3)]^(2)}`

`b = 5`

If we know that
`p = 18` and
`b = 5`, then the height of the rectangle is:

`2\cdot h = p-2\cdot b`

`h = (p-2\cdot b)/(2)`

`h = (p)/(2)-b`

`h = 4`

There are two possible solutions for the other two vertices of the rectangle:

(i) (4, 1), (-1, 1), (ii) (4, -7), (-1, -7)