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.
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, negative 4. E is at 5, negative 4. F is at 2, negative 1. Line BC and line EF intersect at point 0, 1.

Answer 1

The slope of the side of ΔABC that is perpendicular to the side EF is $-\frac{1}{Slope \ of \ EF}$

Response:

• The equation of the side of ΔABC that is perpendicular to EF in slope and intercept form is; y = x + 1

Which is the method used to find the equation of the perpendicular lines?

Given:

Points on ΔABC are; A(4, 2), B(4, 5), C(1, 2)

Points on ΔDEF are; , D(2, (-4)), E(5, (-4)), F(2, -1)

The slope of the side BC is  $\mathbf{\dfrac{5 - 2}{4 - 1} } = 1$

Equation of side BC is y - 2 = 1·(x - 1) = x - 1

y = x - 1 + 2 = x + 1

y = x + 1

Slope of the side EF is  $\dfrac{-1 - (-4)}{2 - 5} =\mathbf{ -1}$

Equation of the side EF is y - (-1) = (-1)·(x - 2)

Which gives;

Equation of EF is; y + 1 = (-1)·(x - 2)

Given that the slope of BC is the negative inverse of the slope of EF, we have;

The line BC is perpendicular to the line EF

• The equation of the side of triangle ABC that is perpendicular to EF which is side BC is; y = x + 1

Learn more about perpendicular lines here:

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