Question

Based on the diagram, can point D be the centroid of triangle ACF? Explain.

Yes, point D is the point of intersection of segments drawn from all three vertices.
Yes, DE is three-quarters of the length of the full segment.
No, DE should be longer than AD.
No, the ratio between AD and DE is 3:1.

Answer 1

a centroid in a triangle, is the point where all the medians meet.

now a peculiar thing about the centroid is that, it cuts all medians in a 2:1 ratio.

so, if that's true, then the median AE, is being cut in two segments AD and DE and AD : DE are on a 2 : 1 ratio, are they?  let's check.

$\bf \stackrel{median~AE}{AD+DE}\qquad AD:DE\implies \cfrac{AD}{DE}\implies \cfrac{12}{4}\implies \cfrac{3}{1}\implies 3:1 \ne 2:1$

Answer 2

A ratio shows us the number of times a number contains another number. The correct option is D.

What is a Ratio?

A ratio shows us the number of times a number contains another number.

A centroid is the point where all the three medians of the triangle intersect. It is also the point at which divides all the median in 2:1 ratio. Therefore, if the ratio of AD:DE is 2:1, then D can be the centroid of the circle.

Now the ratio of AD:DE is,

AD/DE = 12/4 = 3/1

Since the ratio of AD:DE is 3:1. D can not be the centroid of the triangle.

Hence, the correct option is D.

Learn more about Ratios:

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