Question

abc has coordinates A (3, 4), B (-5, 6), and C (0, 4). The triangle is transformed according to the rule ( x , y )→(- x , - y ). Determine how many degrees the original triangle was rotated.

Answer 1

To determine how many degrees the original triangle was rotated, apply the given transformation to the coordinates of the triangle. The original triangle was rotated approximately 53.13 degrees.

Step-by-step explanation:

To determine how many degrees the original triangle was rotated, we need to apply the given transformation to the coordinates of the triangle. The transformation ( x , y ) -> (- x , - y ) reflects each point across the x-axis and y-axis. Applying this transformation to the coordinates of the triangle ABC, we get the new coordinates A' (-3, -4), B' (5, -6), and C' (0, -4).

Next, we can calculate the slope of the line joining points A and A' using the formula: m = (y2 - y1) / (x2 - x1). For point A (3, 4) and A' (-3, -4), the slope is m = (-4 - 4) / (-3 - 3) = (-8) / (-6) = 4 / 3.

The angle of rotation can be found using the arctan function of the slope. Therefore, arctan(4/3) ≈ 53.13 degrees. Hence, the original triangle was rotated approximately 53.13 degrees.