Question

Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-4, -2), B(-2, -2), C(-2, 7), and D(-4, 7).
What is the area of rectangle ABCD?

Answer 1

Join A and C.

Coordinates of sides of triangle = (-4 , -2)  (-2 , -2 )  (-2 , 7)

Area of triangle ABC = 1/2 ( x₁ (y₂ - y₃) + x₂( y₃ - y₁ ) + x₃ (y₁ - y₂))

= 1/2 ( -4 (-2 - 7) + (-2) (7 - (-4)) + (-2) (-4 - (-2))

= 1/2 ( -4 (-9) -2 (11) - 2 (-2) )

= 1/2 ( 36 - 22 + 4 )

= 1/2 ( 36 - 18 )

= 1/2 (18)

= 9 units

Area of triangle ACD = 1/2 ( x₁ (y₂ - y₃) + x₂( y₃ - y₁ ) + x₃ (y₁ - y₂))

Coordinates = ( -4 , -2 )  (-2 , 7 )  ( -4 , 7 )

Area = 1/2 ( -4 (7 - 7 ) + (-2) ( 7 - (-2) ) + (-4) ( -2 - 7 )

= 1/2 ( -4 (0) - 2 (9) - 4 ( - 9 ) )

= 1/2 ( 0 - 18 + 36 )

= 1/2 (18)

= 9 units

Total area = 9 + 9 = 18 units

Answer 2

Answer: 18 square units. trust me