Respuesta :
The correct answer is:
x=4.
Explanation:
The slope of line AB is given by the formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Using the coordinates of A and B, we have
[tex]m=\frac{4-4}{4--3}=\frac{0}{7}=0[/tex]
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.
x=4.
Explanation:
The slope of line AB is given by the formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Using the coordinates of A and B, we have
[tex]m=\frac{4-4}{4--3}=\frac{0}{7}=0[/tex]
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.
Answer: The required equation of line BC is [tex] x=4.[/tex]
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
[tex]m=\dfrac{d-b}{c-a}.[/tex]
So, the slope of the line AB will be
[tex]m=\dfrac{4-4}{4-(-3)}\\\\\Rightarrow m=0.[/tex]
Therefore, the equation of the line AB is
[tex]y-4=m(x-4)\\\\\Rightarrow y-4=0\\\\\Rightarrow y=4.[/tex]
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
[tex]x=4.[/tex]
Thus, the required equation of line BC is [tex] x=4.[/tex]
