Question

What is the area of a rectangle with vertices at ​(−4, 0)​, ​(−3, 1)​ , (0, −2), and (−1, −3)? Enter your answer in the box. Do not round any side lengths.

Answer 1

Given :

Vertices of triangle ​(−4, 0)​, ​(−3, 1)​ , (0, −2), and (−1, −3).

To Find :

The area of a rectangle.

Solution :

Breadth of triangle :

`B = √((-4-(-3))^2+(0-1)^2)\\\\B = √(1^2+1^2)\\\\B = √(2)\ units`

Length of triangle :

`L = √((-4-0)^2+(0-(-2))^2)\\\\L = √(16+4)\\\\L = 2√(5)\ units`

Now, area is given by :

A = L×B

A = √2×2√5

A = 2√10 units

Therefore, the area is 2√10 units.

Hence, this is the required solution.