Answer:
There are two possible solutions for the other two vertices of the rectangle:
(i) (4, 1), (-1, 1), (ii) (4, -7), (-1, -7)
Step-by-step explanation:
Geometrically speaking, the perimeter of a rectangle ([tex]p[/tex]) is:
[tex]p = 2\cdot b + 2\cdot h[/tex] (1)
Where:
[tex]b[/tex] - Base of the rectangle.
[tex]h[/tex] - 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:
[tex]b = \sqrt{[(-1)-4]^{2}+[(-3)-(-3)]^{2}}[/tex]
[tex]b = 5[/tex]
If we know that [tex]p = 18[/tex] and [tex]b = 5[/tex], then the height of the rectangle is:
[tex]2\cdot h = p-2\cdot b[/tex]
[tex]h = \frac{p-2\cdot b}{2}[/tex]
[tex]h = \frac{p}{2}-b[/tex]
[tex]h = 4[/tex]
There are two possible solutions for the other two vertices of the rectangle:
(i) (4, 1), (-1, 1), (ii) (4, -7), (-1, -7)
