Study Guide: Geometry

Question

Triangle ABC has been rotated 90° to create triangle DEF. Write the equation, in slope-intercept form, of the side of triangle ABC that is perpendicular to segment EF.

Picture:

"Triangles ABC and DEF are shown. A is at (4, 2). B is at (4, 5). C is at (1, 2). D is at (2, - 4). E is at (5, - 4). F is at (2, - 1). Line BC and line EF intersect at point 0, 1.

Answer 1

Since we rotated ABC by 90° to get DEF, each side in DEF is perpendicular to the corresponding side in ABC. So, AB and DE are perpendicular, AC and DF are perpendicular, and BC and EF are perpendicular. Now that you know that BC is the side you want, you can figure out the equation of its line, y = mx + b, using the coordinates of its two endpoints, B and C.

First, determine the slope, m, of BC using the slope formula

m = (y_C-y_B)/(x_C-x_B)

Plug the value of m you get into y = mx + b. Next, using either endpoint (B or C), plug the x and y values into your y = mx + b equation and solve for b.