Answer:
[tex]Z(x,y) = (-7 ,1)[/tex]
Step-by-step explanation:
Given
[tex]X(-2, 6); Y(-10, -2).[/tex]
[tex]Ratio= 5:3[/tex]
Required
Point Z
Given that the line segment XY is divided into ratio;
The coordinates of point Z can be calculated using ratio formula given below
[tex]Z(x,y) = (\frac{mx_2 + nx_1}{m+n} ,\frac{my_2 + ny_1}{m+n})[/tex]
Where m and n are the ratio; m = 5 and n = 3
[tex](x_1, y_1) = (-2, 6); \\(x_2, y_2) = (-10, -2).[/tex]
So,
[tex]Z(x,y) = (\frac{mx_2 + nx_1}{m+n} ,\frac{my_2 + ny_1}{m+n})[/tex] becomes
[tex]Z(x,y) = (\frac{5 * -10 + 3 * -2}{5+3} ,\frac{5 * -2 + 3 * 6}{5+3})[/tex]
[tex]Z(x,y) = (\frac{-50 + -6}{8} ,\frac{-10 + 18}{8})[/tex]
[tex]Z(x,y) = (\frac{-56}{8} ,\frac{8}{8})[/tex]
[tex]Z(x,y) = (-7 ,1)[/tex]
Hence, the coordinates of Z are (-7,1)
