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12 days ago

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?

Mathematics

2 answers:

Inessa [3.9K]12 days ago

8 0

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

Step-by-step explanation: As shown in the provided diagram, lines AB and BC intersect at right angles at point B. The coordinates for points A and B are (-3, 4) and B(4, 4). We need to determine the equation for line BC.

The formula for determining the slope of a line connecting points (a, b) and (c, d) is given by

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

The slope of line AB is

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

Consequently, the equation of line AB is

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

Since the equation y = constant characterizes a line parallel to the X-axis, its perpendicular counterpart must align with the Y-axis.

Hence, it will have the form of

x = constant.

Given that line BC is perpendicular to line AB and passes through point (4, 4), it follows that

$x=4.$

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

AnnZ [3.8K]12 days ago

4 0

The correct answer is:

x=4.

Explanation:

The slope between points A and B is calculated using the formula
$m=\frac{y_2-y_1}{x_2-x_1}$
Using the coordinates for points A and B, we can determine
$m=\frac{4-4}{4--3}=\frac{0}{7}=0$
Lines that are perpendicular have slopes that are negative reciprocals. The slope of line AB is 0/7, which has an undefined reciprocal of 7/0. This indicates that the line is vertical. The equation for vertical lines takes the form x=c, which is constant; for line B, with coordinates (4, 4), this results in x=4.

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