A triangle has corners at #(3 ,4 )#, #(6 ,7 )#, and #(2 ,8 )#. How far is the triangle's centroid from the origin?
1 Answer
Apr 24, 2017
Explanation:
#"the first step is to find the coordinates of the centroid"#
#"the coordinates are the " color(blue)"average"# of the x and y coordinates of the given points.
#x_("centroid")=1/3(3+6+2)=11/3#
#y_("centroid")=1/3(4+7+8)=19/3#
#"coordinates of centroid "=(11/3,19/3)# the distance between the centroid and the origin is.
#d=sqrt((x_("centroid"))^2+(y_("centroid"))^2#
#color(white)(d)=sqrt((11/3)^2+(19/3)^2)#
#color(white)(d)=sqrt(121/9+361/9)#
#color(white)(d)=sqrt(482/9)#
#color(white)(d)=1/3sqrt482~~7.32" to 2 dec. places"#
