Answer:
Z(-0.2, 2.2).
Step-by-step explanation:
We will use section formula when a point, say P, divides any segment ,say AB, internally in the ratio m:n.
[tex][x=\frac{mx_2+nx_1}{m+n}, y= \frac{my_2+ny_1}{m+n}][/tex]
We have been given the points of segment XY as X at (-2,1) and Y at (4,5) and ratio is 3:7.
[tex](x_1, y_1)=(-2,1)[/tex]
[tex](x_2, y_2)=(4,5)[/tex]
[tex]m:n=3:7[/tex]
Upon substituting coordinates of our given points in section formula we will get,
[tex][x=\frac{(3*4)+(7*-2)}{3+7}, y= \frac{3*5+7*1}{3+7}][/tex]
[tex][x=\frac{12-14}{10}, y= \frac{15+7}{10}][/tex]
[tex][x=\frac{-2}{10}, y= \frac{22}{10}][/tex]
[tex][x=-0.2, y= 2.2][/tex]
Therefore, coordinates of point Z will be (-0.2, 2.2).
