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] at Q
Required
Determine Q
This can be calculated using line ratio formula;
[tex]Q(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})\\[/tex]
Where:
[tex](x_1,y_1) = (-10,12)[/tex]
[tex](x_2,y_2) = (6,8)[/tex]
[tex]m:n = 2:3[/tex]
So, we have:
[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 are:
[tex]Q(x,y) = (\frac{-18}{5},\frac{52}{5})[/tex]
