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 differences in \(x\) - coordinates

For two adjacent vertices \((x_1,y_1)\) and \((x_2,y_2)\), the difference in \(x\) - coordinates \(\Delta x=x_2 - x_1\).
For example, between \((5,17)\) and \((10,20)\), \(\Delta x=10 - 5=5\); between \((10,20)\) and \((18,9)\), \(\Delta x=18 - 10 = 8\).

Step2: Calculate differences in \(y\) - coordinates

The difference in \(y\) - coordinates \(\Delta y=y_2 - y_1\).
Between \((5,17)\) and \((10,20)\), \(\Delta y=20 - 17 = 3\); between \((10,20)\) and \((18,9)\), \(\Delta y=9 - 20=- 11\).
When using the box - method (also known as the rectangle - subtraction method for finding the area of a polygon given coordinates), the right - triangles (cut - outs) are formed based on the horizontal and vertical distances between the vertices of the parallelogram.
The horizontal and vertical differences between vertices \((10,20)\) and \((18,9)\) give a right - triangle with legs \(|18 - 10| = 8\) and \(|9 - 20|=11\) (we take absolute values since lengths are non - negative).

Answer:

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