We need to find the point which cuts X and Y in 3/4.
Let, coordinates of the point is P.
So, coordinates of P is :
[tex][(\dfrac{mx_1+nx_2}{m+n}),(\dfrac{my_1+ny_2}{m+n})]\\\\(\dfrac{3x_1+4x_2}{3+4}),(\dfrac{3y_1+4y_2}{3+4})\\\\(\dfrac{3(1)+4(9)}{3+4}),(\dfrac{3(-6)+4(10)}{3+4})\\\\(\dfrac{39}{7},\dfrac{22}{7})[/tex]
Therefore, the coordinate of the point 3/4 of the way from X(1, −6) to Y(9, 10)
is [tex](\dfrac{39}{7},\dfrac{22}{7})[/tex] .
Hence, this is the required solution.
