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. You must show all work to receive credit.

Answer 1

Given:

Triangle ABC has been rotated 90° to create triangle DEF.

To find:

The equation, in slope-intercept form, of the side of triangle ABC that is perpendicular to segment EF.

Solution:

It is given that triangle ABC has been rotated 90° to create triangle DEF. It means the angle on the intersection of lines BC and EF is 90 degrees.

So, the line BC is perpendicular to segment EF.

The line BC passes through the points B(4,5) and C(1,2). So, the equation of the line BC is:

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-5=\dfrac{2-5}{1-4}(x-4)$

$y-5=\dfrac{-3}{-3}(x-4)$

$y-5=1(x-4)$

On further simplification, we get

$y-5=x-4$

$y=x-4+5$

$y=x+1$

Therefore, the required equation is $y=x+1$.