Question

Line AB and BC for a right angle at point B. If A(-3,4) and B(4,4) what is the equation of line BC?

Answer 1

Answer:  The required equation of line BC is $x=4.$

Step-by-step explanation:  As shown in the attached figure, lines AB and BC meet at right angle at the point B. The co-ordinates of point A and B are (-3, 4) and B(4, 4).

We are to find the equation of line BC.

We know that the slope of a line passing through the points (a, b) and (c, d) is given by

$m=\dfrac{d-b}{c-a}.$

So, the slope of the line AB will be

$m=\dfrac{4-4}{4-(-3)}\\\\\Rightarrow m=0.$

Therefore, the equation of the line AB is

$y-4=m(x-4)\\\\\Rightarrow y-4=0\\\\\Rightarrow y=4.$

Since y = constant is the equation of a line parallel to X-axis, so its perpendicular line will be parallel to Y-axis.

So, its equation will be of the form

x = constant.

Since the line BC is perpendicular to AB passing through the point (4, 4), so we must have

$x=4.$

Thus, the required equation of line BC is $x=4.$

Answer 2

The correct answer is:

x=4.

Explanation:

The slope of line AB is given by the formula
$m=\frac{y_2-y_1}{x_2-x_1}$

Using the coordinates of A and B, we have
$m=\frac{4-4}{4--3}=\frac{0}{7}=0$

Perpendicular lines have slopes that are negative reciprocals. Since the slope of AB is 0/7, the reciprocal is 7/0, which is undefined.

Any line with an undefined slope is a vertical line. This will be a vertical line that passes through point B.

Vertical lines have the equation x=c, where c is a constant; since it runs through B, which has coordinates (4, 4), this means the equation is x=4.