Question

(04.02 MC) 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

Answer:

$y =1 -x$

Step-by-step explanation:

Given

$A = (4,2)$

$B = (4,5)$

$C = (1,2)$

$D = (2,-4)$

$E = (5,-4)$

$F = (2,-1)$

Required

Determine the equation of line EF perpendicular to BC at intersect 0,1

The question has missing attachment but it can still be solved;

First, we need to determine the slope of BC using

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where

$(x_1,y_1) = (4,5)$ Point B

$(x_2,y_2) = (1,2)$ Point C

Substitute these values in the above formula

$m_1 = \frac{2 - 5}{1 - 4}$

$m_1 = \frac{- 3}{- 3}$

$m_1 = 1$

Next is to determine the slope of EF;

Since, there are perpendicular: we have

$m_1 * m_2 = -1$

Substitute -1 for m1

$1 * m_2 = -1$

$m_2 = -1$

Next, is to determine the slope of EF at intersect (0,1).

The formula to use is:

$y - y_1 = m_2(x - x_1)$

In this case;

$(x_1,y_1) = (0,1)$

Substitute values for m2, x1 and y1

$y - 1 = -1(x - 0)$

$y - 1 = -1(x)$

Open the bracket

$y - 1 = -x$

Add 1 to both sides

$y - 1 +1 =1 -x$

$y =1 -x$

Hence;

The equation is $y =1 -x$