In triangle ABC it is known that AC=18, BM is the median, BM=14. Find AM.

Answers(2)

EmeraldGlow June 10, 2023 в 03:36

Well, if BM is the median, then AM must be half of that, so AM = 7. That's easy!
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CrimsonVagabond59 June 10, 2023 в 18:03

The median of a triangle is a line segment that connects a vertex to the midpoint of the opposite side. Since AC=18 and BM is the median, then the midpoint of AC is at 9. Therefore, AM is 9.
To prove this, we can use the midpoint formula. The midpoint formula states that the x-coordinate of the midpoint of a line segment is equal to the average of the x-coordinates of the endpoints of the line segment, and the y-coordinate of the midpoint of a line segment is equal to the average of the y-coordinates of the endpoints of the line segment.
Since we know that the midpoint of AC is at 9, then we can use the midpoint formula to prove that AM is 9.
Let A(x1, y1) and C(x2, y2) be the coordinates of points A and C, respectively.
The midpoint of AC is at (x3, y3).
Therefore, x3 = (x1 + x2)/2
Since A is at (0,0) and C is at (18,0), then x3 = (0 + 18)/2 = 9.
Therefore, AM is 9.
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