Question

area in the coordinate plane quick check
to the nearest tenth, what is the area of the rectangle abcd with vertices a(-3, -2), b(-5, 2), c(3, 6), and d(5, 2)? (1 point)
26.0
40
32.0
1,460.0

Explanation:

Step1: Find length of base

Use distance formula for two - points. For points \(B(-5,2)\) and \(D(5,2)\), \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{(5+5)^2+(2 - 2)^2}=10\).

Step2: Find length of height

For points \(B(-5,2)\) and \(C(3,6)\), \(d=\sqrt{(3 + 5)^2+(6 - 2)^2}=\sqrt{64 + 16}=\sqrt{80}\approx8.9\).

Step3: Calculate area of rectangle

Area \(A=\text{base}\times\text{height}=10\times8.9 = 89\) (This calculation has error in original options. Correct way using vector cross - product or Shoelace formula:
Let \(\vec{AB}=(-5+3,2 + 2)=(-2,4)\) and \(\vec{AD}=(5 + 3,2+2)=(8,4)\)
Area \(A=\vert(-2)\times4-4\times8\vert=\vert-8 - 32\vert = 40\))

Answer:

40