Values of x and y will be 12 and 5 respectively.
It's given in the question,
Since, expression for the coordinates of a point (h, k) which divides the segment joining points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in the ratio of m : n is given by,
h = [tex]\frac{mx_2+nx_1}{m+n}[/tex]
k = [tex]\frac{my_2+my_1}{m+n}[/tex]
Since, R is a point on segment QS dividing in the ratio of 3 : 2, coordinates of R will be,
[tex]8=\frac{3x+2\times 2}{3+2}[/tex]
[tex]8=\frac{3x+4}{5}[/tex]
[tex]3x+4=40[/tex]
[tex]3x=36[/tex]
[tex]x=12[/tex]
Similarly, [tex]3=\frac{3y+2\times 0}{3+2}[/tex]
[tex]3=\frac{3y}{5}[/tex]
[tex]3y=15[/tex]
[tex]y=5[/tex]
Therefore, values of x and y will be 12 and 5 respectively.
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