Question

Please help me asap!

Answer 1

ANSWER

$y = 2x - 4$

EXPLANATION

To find the equation of BC, we must find the slope and use the point B(4,4) with the slope to find the equation.

We know the slope of BC is perpendicular to the slope of AB.

But the slope of AB
$= \frac{4 - 5}{4 - 2}$

$= - \frac{1}{2}$

The slope of BC is the negative reciprocal of the slope of AB, which is
$= - \frac{ 1 }{ - \frac{ 1}{2} }$
$= - 1 \times - \frac{2}{1} = 2$

The equation in slope intercept form is given by,

$y = mx + c$

This implies that,

$y = 2x + c$

The point B(4,4) lies on this line so it must satisfy its equation,

$4 = 2(4) + c$

$4 = 8 + c$

$c = 4 - 8 = - 4$

The required equation is,

$y = 2x - 4$

The correct answer is A