Answer:
[tex]Q(x,y) = (\frac{-18}{5},\frac{52}{5})[/tex]
Step-by-step explanation:
Given
[tex]M = (-10,12)[/tex]
[tex]T = (6,8)[/tex]
[tex]Ratio = 2:3[/tex]
Required
Determine the coordinate of Q
The question will be answered using the following line ratio formula
[tex]Q(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
Where
[tex]m:n = 2:3[/tex]
[tex](x_1,y_1) = (-10,12)[/tex]
[tex](x_2,y_2) = (6,8)[/tex]
[tex]Q(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex] becomes
[tex]Q(x,y) = (\frac{2 * 6 + 3 * -10}{2+3},\frac{2 * 8 + 3 * 12}{2+3})[/tex]
[tex]Q(x,y) = (\frac{12 - 30}{5},\frac{16+36}{5})[/tex]
[tex]Q(x,y) = (\frac{-18}{5},\frac{52}{5})[/tex]
Hence,, the coordinates of Q is
[tex]Q(x,y) = (\frac{-18}{5},\frac{52}{5})[/tex]
