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lapo4ka [179]
3 years ago
8

Given that L is the centroid of triangle FGH, find LG.

Mathematics
1 answer:
olga55 [171]3 years ago
5 0
Well the centroid is the point that connects the median of a side with the opposite vertex. This means that each line is split i half. Notice that line HG is split in half by point K. that means that each of the segments that K splits is equal. so we know
HK = KG

and we know
HK = 3x
KG = x + 8

since
HK = KG then
3x = x + 8
2x = 8
x = 4

now we have x. we know that the each line that runs from a midpoint to a vertex is seperated by the centroid. the 2 line segments are a 2:1 ratio. so
2*JL = 1LG

we know
JL = x + 3

so
2 * (4 + 3) = LG
LG = 14
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Step-by-step explanation:

You want to find the equation for a line that passes through the two points:

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The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (0,2), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=0 and y1=2.

Also, let's call the second point you gave, (-4,0), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-4 and y2=0.

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m= 0 - 2-4 - 0 or... m= -2-4 or... m=1/2

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=1/2x+b

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To find b, think about what your (x,y) points mean:

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(-4,0). When x of the line is -4, y of the line must be 0.

Because you said the line passes through each one of these two points, right?

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So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

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