Find the point that partitions line segment AB withendpoints A(-2, 1) and B(4,6) in a ratio of 1:2.

Answer:The coordinates of [tex](x,y)  = (0,\frac{8}{3} )[/tex]Step-by-step explanation:The coordinates of the points are given as A(-2, 1) and B(4,6).The ratio is 1 : 2Le t us assume the point is M (x,y).⇒ AM : MB =  1 : 2Now, Using SECTION FORMULA:[tex](x,y)  = (\frac{m1 x2 + m2 x1}{m1 + m2} ,\frac{m1 y2 + m2 y1}{m1 + m2})[/tex]Using m1 : m2 = 1 : 2Here, we get [tex](x,y)  = (\frac{1(4)  + 2(-2)}{1 + 2} ,\frac{1(6) + 2(1)}{1 + 2})\\\implies (x,y) = (\frac{4-4}{3} ,\frac{6+2}{3} )\\or, (x,y) = (0 ,\frac{8}{3} )[/tex]Hence, the coordinates of [tex](x,y)  = (0, \frac{8}{3} )[/tex]