Answer:
[tex]B =(3.3,1.7)[/tex]
Step-by-step explanation:
Given
[tex]A(x_1,y_1) = (-4,-2)[/tex]
[tex]P(x,y) = (2,1)[/tex]
[tex]m : n = 9 : 2[/tex]
Required
The coordinates of [tex]B(x_2,y_2)[/tex]
The line segment from ratio is calculated as:
[tex](x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
Substitute: A, P, m and n
[tex](2,1) = (\frac{9 * x_2 + 2*-4}{9+2},\frac{9*y_2 +2 *-2}{9+2})[/tex]
[tex](2,1) = (\frac{9x_2 -8}{11},\frac{9y_2 -4}{11})[/tex]
Multiply through by 11
[tex](22,11) = (9x_2 -8,9y_2 -4)[/tex]
By comparison:
[tex]9x_2 - 8 = 22[/tex]
[tex]9y_2 - 4 = 11[/tex]
So, we have:
[tex]9x_2 - 8 = 22[/tex]
[tex]9x_2 = 22 +8[/tex]
[tex]9x_2 = 30[/tex]
Solve for x2
[tex]x_2 = 30/9[/tex]
[tex]x_2 = 3.3[/tex]
[tex]9y_2 - 4 = 11[/tex]
[tex]9y_2 = 11+4[/tex]
[tex]9y_2 = 15[/tex]
Solve for y2
[tex]y_2 =15/9[/tex]
[tex]y_2 =1.7[/tex]
So, the coordinates of B is:
[tex]B =(3.3,1.7)[/tex]
