Question

ordinate geometry > lesson 3 area in the coordinate plane back to intro page determine the coordinates of rectangle abcd. use the coordinates to compute the area of the rectangle. (1 point) units²

Explanation:

Step1: Assume rectangle vertices

Since no coordinates are given in the image, assume the rectangle has vertices \(A(x_1,y_1)\), \(B(x_2,y_1)\), \(C(x_2,y_2)\), \(D(x_1,y_2)\) in a coordinate - plane. The length \(l=\vert x_2 - x_1\vert\) and width \(w=\vert y_2 - y_1\vert\).

Step2: Use area formula

The area formula of a rectangle is \(A = l\times w\). Without specific coordinates, if we assume the length along the x - axis is \(a\) units and the length along the y - axis is \(b\) units, then \(A=a\times b\). But since no values are provided for the sides from the image, we need more information. However, if we assume for the sake of a general example that we find two adjacent vertices \((x_1,y_1)\) and \((x_2,y_2)\) such that the length \(l=\vert x_2 - x_1\vert = 4\) and width \(w=\vert y_2 - y_1\vert = 3\).
\[A = l\times w=4\times3 = 12\]

Answer:

12 (assuming sample side - lengths as described above; actual answer depends on given coordinates)