Answer: AB and BC form a right angle at point B, so BC is perpendicular to AB. To find the equation of BC, we can use the slope-point formula, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.
The slope of a line perpendicular to AB can be found by finding the negative reciprocal of the slope of AB. To find the slope of AB, we need to find the difference in the y-coordinates and divide it by the difference in the x-coordinates:
m_AB = (y2 - y1) / (x2 - x1)
= (4 - (-1)) / (4 - (-3))
= 5 / 7
The slope of a line perpendicular to AB is the negative reciprocal of m_AB:
m_BC = -1 / m_AB = -1 / (5/7) = -7/5
Now that we have the slope of BC, we can use the slope-point formula to find the equation of BC. We'll use the point B = (4, 4) as (x1, y1):
y - 4 = -7/5 (x - 4)
y = -7/5 x + 4(7/5) + 4
y = -7/5 x + 36/5
So the equation of BC is y = -7/5 x + 36/5.
Explanation: