Question

A rectangle has points A (-5,2), B(1,6), C(9,-6), and D(3,-10). Find the area.

Answer 1

AB = √((1 - (-5))² + (6 - 2)²) = √(6² + 4²)

= √(36 + 16) = √52 = 2√13

AC = √((9 - (-5))² + (-6 - 2)²) = √(14² + (-8)²)

= √(196 + 64) = √260 = 2√65

Ares of rectangle ABCD = (2√13)(2√13√5)

= 4(13√5) = 52√5

Answer 2

To find the area of the rectangle, calculate the length of the sides and multiply them together.

Step-by-step explanation:

The area of the rectangle can be found by using the formula for the area of a rectangle: length multiplied by width. To calculate the length, we can find the distance between points A and B, which is the same as the distance between points C and D. This can be done using the distance formula: √((x2-x1)^2 + (y2-y1)^2). Similarly, we can find the distance between points A and D, which is the same as the distance between points B and C. Once we have the lengths of the sides, we can calculate the area by multiplying the length and width together.

Length of the sides:

• AB = CD = √((1-(-5))^2 + (6-2)^2) = √(6^2 + 4^2) = 2√10
• AD = BC = √((3-(-5))^2 + (-10-2)^2) = √(8^2 + (-12)^2) = √(64 + 144) = √208

Now we can calculate the area:

Area = Length × Width = AB × AD = 2√10 × √208 = 2√(10 × 52) = 2√(10 × 4 × 13) = 4√26 square units.