Triangle ABC has been rotated 90 degrees to create triangle DEF. Using the image below, prove that perpendicular lines have opposite and reciprocal slopes. You must show all your work to receive credit.
Could someone please help me with this essay question. I am so confused!

Question

Triangle ABC has been rotated 90 degrees to create triangle DEF. Using the image below, prove that perpendicular lines have opposite and reciprocal slopes. You must show all your work to receive credit.
Could someone please help me with this essay question. I am so confused!

anonymous · Answer

attachment

anonymous · Answer

Please help I am so frustrated.

whpalmer4 · Answer

Find the slope of the hypotenuse of each triangle.  Compare their slopes.

whpalmer4 · Answer

formula for slope of a line going through points $(x_1,y_1)\text{ and }(x_2,y_2)$ is
$$m = \frac{y_2-y_1}{x_2-x_1}$$I usually adopt the convention that the point on the left is the one I call $(x_1,y_1)$ but it doesn't matter so long as you are consistent with your identification of the point when finding the slope.