Question

A triangle has corners at `(1 ,4 )`, `(7 ,5 )`, and `(3 ,2 )`. How far is the triangle's centroid from the origin?

Answer 1

distance of centroid from origin is: `" "11/3sqrt2`

Explanation:

`color(blue)("Determine the Centroid - Shortcut method")`

The triangle's centroid is the mean point.

So mean `x" is " (1+3+7)/3 = 11/3 ->3 2/3`

Mean `y" is "(2+4+5)/3 = 11/3-> 3 2/3`

`color(blue)("Centroid"->(x,y)=(11/3,11/3))`
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`color(blue)("Determine distance of centroid from origin")`

Using Pythagoras

`"distance (d)" = sqrt(2(11/3)^2)" "=" "11/3sqrt2`

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`color(brown)("If you so chose you could check this by building")`
`color(brown)("equations of lines and solving for simultaneous equations")`