Question

What is the area of the rectangle with vertices at (-6,2), (2,-2), (5,4), and (-3,8)?​

Answer 1

Answer:

59.97 square units .

Explanation:

We are given the coordinates of the rectangle;

(-6,2), (2,-2), (5,4), and (-3,8)

• To get the area of the rectangle, we can first calculate the length and the width of the rectangle.
• To get the length and the width we are going to use the formula for getting magnitude;
• Magnitude = $\sqrt{((x1-x2)^2 + (y1-y2)^2)}$

Thus;

Between (-6,2) and  (2,-2)

Magnitude = $\sqrt({(-4)^2+8^2)}$

                  $=\sqrt{80}$

                 $=8.94$

Between (2,-2) and (5,4)

Magnitude$=\sqrt{(6^2+3^2)}$

                      $=\sqrt{45}$

                      $=6.708$

Therefore, the length of the rectangle is 8.94 units while the width is 6.708 units

But area of a rectangle is given by;

Area = Length × Width

Therefore;

Area = 6.708 units × 8.94 units

        = 59.97 square units

Therefore the area of the rectangle is 59.97 square units .