Question

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

Answer 1

59.97 square units .

Step-by-step 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 =
  `√(((x1-x2)^2 + (y1-y2)^2))`

Thus;

Between (-6,2) and (2,-2)

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

`=√(80)`

`=8.94`

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

Magnitude
`=√((6^2+3^2))`

`=√(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 .