Question

coordinate geometry > coordinate geometry unit test
a (-3, -1) b (-2, -4) d (3, 1) c (4, -2)
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use the coordinates to compute the approximate area of the rectangle.
(1 point)
30 units²
40 units²
20 units²
10 units²

Explanation:

Step1: Find the length of the base

The base can be calculated by the difference in \(x -\)coordinates. For example, between \(A(-3,-1)\) and \(D(3,1)\). The horizontal distance \(b\):

$$b=\vert x_D - x_A\vert=\vert3-(-3)\vert = 6$$

Step2: Find the height

The height can be calculated by the difference in \(y -\)coordinates. For example, if we consider a vertical - like distance. Another way is to use the formula for the area of a parallelogram (since the figure is a quadrilateral, and if we assume it's a parallelogram - by using the shoelace formula in a simpler way for approximation). If we use the base \(b = 6\) and assume a height \(h\approx5\) (by counting the grid units vertically from the lower - most point \(B(-2,-4)\) to the upper - most point \(D(3,1)\), the vertical distance \(\vert y_D - y_B\vert=\vert1-(-4)\vert = 5\)).
The area of a parallelogram \(A = b\times h\)

$$A=6\times5 = 30$$

Answer:

\(30\ units^{2}\)