Question

a parallelogram has coordinates of (5, 17), (10, 20), (18, 9), and (13, 6). which right triangle represents one of the cutouts from the box method?

Explanation:

Step1: Calculate horizontal and vertical distances

For two adjacent vertices \((x_1,y_1)\) and \((x_2,y_2)\), the horizontal distance \(d_x=\vert x_2 - x_1\vert\) and vertical distance \(d_y=\vert y_2 - y_1\vert\).
Take \((5,17)\) and \((10,20)\): \(d_x=\vert10 - 5\vert = 5\), \(d_y=\vert20 - 17\vert=3\).
Take \((10,20)\) and \((18,9)\): \(d_x=\vert18 - 10\vert = 8\), \(d_y=\vert9 - 20\vert = 11\).
Take \((18,9)\) and \((13,6)\): \(d_x=\vert13 - 18\vert=5\), \(d_y=\vert6 - 9\vert = 3\).
Take \((13,6)\) and \((5,17)\): \(d_x=\vert5 - 13\vert = 8\), \(d_y=\vert17 - 6\vert=11\).

Step2: Analyze the right - triangle side lengths

The box - method cut - outs (right - triangles) for a parallelogram formed by the given vertices will have side lengths corresponding to the differences in \(x\) and \(y\) coordinates of adjacent vertices.
The right - triangle with legs \(8\) and \(11\) (first triangle in the given options) can be formed from the differences in coordinates of non - adjacent vertices (e.g., when considering the "spread" of the parallelogram in the coordinate plane).

Answer:

The right - triangle with legs \(8\) and \(11\) (the first triangle in the given set of options) represents one of the cutouts from the box method.