M is the centroid (center of gravity) of △ABC, line k goes thru M and intersects AB and AC . The distances of the vertices B and

Question

vekshin1

4 years ago

10

M is the centroid (center of gravity) of △ABC, line k goes thru M and intersects AB and AC . The distances of the vertices B and

C from line k are 17 and 13 respectively. Find the distance of the vertex A from line k.

Mathematics

1 answer:

lana [24] · Answer 1 · 2021-12-21T13:56:19+03:00

Answer:

30

Step-by-step explanation:

The midpoint of BC will be a distance from line k that is the average of the distances of B and C: (17+13)/2 = 15. Call that midpoint P. We know distance MP is half of distance MA. This same relationship will hold with respect to the distances from P and A to any line through M. That is, the distance from line k (through M) is twice the distance from P to line k: 30 units.