Explanation:
To prove analytically that AC is not perpendicular to BC, we can use the slope-intercept form of the equation of a line.
First, let's calculate the slopes of the two lines AC and BC. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1)
For line AC:
AC: A(-5, 8) and C(-3, -2)
m_AC = (-2 - 8) / (-3 - (-5))
= (-2 - 8) / (-3 + 5)
= -10 / 2
= -5
For line BC:
BC: B(3, 2) and C(-3, -2)
m_BC = (-2 - 2) / (-3 - 3)
= (-2 - 2) / (-3 + 3)
= -4 / 0
The slope of line BC is undefined (division by zero), indicating that it is a vertical line.
Since the slopes of AC and BC are not negative reciprocals of each other (as required for two lines to be perpendicular), we can conclude that AC is not perpendicular to BC.
Therefore, AC is not perpendicular to BC analytically.