Answer:
the equation of line BC is y = (-7/5)x + (48/5).
Explanation:
To find the equation of the line that passes through points B and C, we first need to determine the coordinates of point C. Since the angle at B is a right angle, we can use the slope of line AB to find the slope of line BC.
The slope of line AB is:
mAB = (yB - yA) / (xB - xA)
= (4 - (-1)) / (4 - (-3))
= 5/7
Since lines AB and BC are perpendicular, the slope of line BC is the negative reciprocal of the slope of line AB:
mBC = -1 / mAB
= -7/5
Now we can use the point-slope form of the equation of a line to find the equation of line BC. We can use point B as the known point, since we already know its coordinates:
y - yB = mBC(x - xB)
Substituting the values we have:
y - 4 = (-7/5)(x - 4)
Expanding and simplifying:
y - 4 = (-7/5)x + (28/5)
y = (-7/5)x + (48/5)