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

Answer 1

Violet Aldrich

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

#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(white)(.)#

#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")#

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Answer 2

Sophia Alfred

The distance from the centroid of the triangle formed by the points (1, 4), (7, 5), and (3, 2) to the origin is approximately ( \frac{5}{3} ) units.

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Answer from HIX Tutor

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