Question

ABC has coordinates A=(9,4) B=(26,-3) and C=(14,17). If AD is the median of ABC, is it also an altitude? Why or Why not?

A. Yes, because the median of a triangle is always an altitude.
B. No, because the median and altitude of a triangle are different segments.
C. Yes, because the coordinates of A and D suggest it's an altitude.
D. No, because the coordinates of A and D suggest it's a median.

Answer 1

AD being a median does not necessarily make it an altitude. To be an altitude, AD would need to be perpendicular to BC, and there is insufficient information to determine that solely based on it being a median.

Step-by-step explanation:

The question asks if AD is the median of triangle ABC, whether it is also an altitude, given the coordinates of points A, B, and C. To establish if AD is an altitude, we would need to check if AD is perpendicular to BC. Since the question does not provide the coordinates of D explicitly, and we do not have enough information to mathematically determine if AD and BC are perpendicular, we cannot conclude that AD is an altitude just from the information about it being a median.

For an altitude, we would expect it to intersect BC at a right angle, but we cannot assume it does only because AD is a median. Therefore, the correct answer would be No, because the median and altitude of a triangle are different segments, unless further information indicates that the median is also an altitude.