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 : 2
Le t us assume the point is M (x,y).
⇒ AM : MB = 1 : 2
Now, 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 : 2
Here, 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]
