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

• B(4,5)
• C(1,2)

Finding slope

$\\ \rm{:}\twoheadrightarrow Slope=m=\dfrac{y_2-y_1}{x_2-x_1}$

$\\ \rm{:}\twoheadrightarrow m=\dfrac{2-5}{1-4}$

$\\ \rm{:}\twoheadrightarrow m=\dfrac{-3}{-3}$

$\\ \rm{:}\twoheadrightarrow m=1$

Now

$\\ \rm{:}\twoheadrightarrow y-5=1(x-4)$

SolVing

$\\ \rm{:}\twoheadrightarrow y-5=x-4$

$\\ \rm{:}\twoheadrightarrow y=x-4+5$

$\\ \rm{:}\twoheadrightarrow y=x+1$

Answer 2

Answer:

• y = x + 1

Step-by-step explanation:

As per picture, EF ⊥ BC.

B has coordinates (4, 5) and C has coordinates (1, 2).

Slope of the line BC:

• m = (5 - 2)/(4 - 1) = 3/3 = 1

Use point-slope formula and one of the coordinate pairs:

• y - 5 = 1(x - 4)
• y = x - 4 + 5
• y = x + 1