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In ABC, and intersect each other at point Q. According to a theorem on medians, Q divides in the ratio 2 : 1. What are the coordinates of Q?
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May 13, 2019
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In ABC, and intersect each other at point Q. According to a theorem on medians, Q divides in the ratio 2 : 1. What are the coordinates of Q?
Mathematics
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Nick Rupley
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The point of intersection of medians is a center of triangle ABC. That means that
.
If A(1,-5), B(3,-2) and C(7,-5) the Q coordinates are:
Answer:
and the correct choice is D.
Anna Jeanine
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May 15, 2019
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Anna Jeanine
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The answer is the
fourth choice
-
(3.67, -4)
Since Q is the center of gravity of the triangle ABC, we can use this relationship - vecQA + vecQB + vecQC = vec0 : we will deduct the coordinates of A, B, and C from x and y of Q to get its coordinate.
vecQA = (x-3, y+2)
vecQB = (x-1, y+5)
vecQC = (x-7, y+5)
vec0 = (0, 0)
This will be equivalent to
(x-3) + (x-1) + (x-7) = 0, and (y+2) + (y+5) + (y+5) = 0
3x - 11 = 0, and 3y + 12 = 0
x = 11/3 or 3.67, and y = 12/3 or 4
The coordinates of Q are (3.67, 4)
Dsalaj
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May 18, 2019
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