Using the endpoints A(5,3) and B(-4,-3), how do you partition the line segment into the ratio 1:2 ?

1 Answer
Jim G.
Nov 29, 2017

#(2,1)#

Explanation:

#"using the "color(blue)"section formula"#

#"given the endpoints of a line being partioned"#
#"in the ratio m:n"#

#A(x_1,y_1)" and "B(x_2,y_2)#

#"then the coordinates of the point partitioning the line are"#

#•color(white)(x)[(mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n)]#

#"here "(x_1,y_1)=(5,3)" and "(x_2,y_2)=(-4,-3)#

#"the ratio "m:n=1:2#

#(((1xx-4)+(2xx5))/(1+2),((1xx-3)+(2xx3))/(1+2))#

#=(6/3,3/3)=(2,1)#

#"the point "(2,1)" partitions the line in the ratio "1:2#

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