Answer:
Option (C)
Step-by-step explanation:
AB and BC are perpendicular to each other at point B.
Ordered pairs representing points A and B are (-3, -1) and (4, 4)
Slope of AB, [tex](m_1) = \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]=\frac{(4+1)}{4+3}[/tex]
[tex]=\frac{5}{7}[/tex]
Let the slope of perpendicular line BC = [tex]m_2[/tex]
By the property of perpendicular lines,
[tex]m_1\times m_2=-1[/tex]
[tex]\frac{5}{7}\times m_2=-1[/tex]
[tex]m_2=-\frac{7}{5}[/tex]
Equation of line BC → y - y' = m₂(x - x')
[tex]y-4=(-\frac{7}{5})(x-4)[/tex]
y = [tex]-\frac{7}{5}x+\frac{28}{5}+4[/tex]
5y = -7x + 28 + 20
7x + 5y = 48
-7x - 5y = -48
Option (C) will be the answer.
