Discussion
The points A(4, 7), B(p, 3) and C(7, 3) are the vertices of a right triangle with the right angle at B. The value of p is:
Answer: B
If the right angle is at B, then the sides AB and BC are perpendicular. The product of their slopes must be -1.
Slope of AB = \(\frac{3-7}{p-4} = \frac{-4}{p-4}\).
Slope of BC = \(\frac{3-3}{7-p} = \frac{0}{7-p} = 0\).
A slope of 0 means BC is a horizontal line. For AB to be perpendicular to a horizontal line, it must be a vertical line. A vertical line has an undefined slope, which happens when its denominator is 0.
So, p - 4 = 0, which means p = 4.
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