Respuesta :
Answer:
- The coordinates of C is (3,2)
- The coordinates of D is (11/5,14/5)
Step-by-step explanation:
Given
A(1,4) and B(6,-1)
Required
a. Point C divide AB in ratio 2:3
b. Point D divide AC in ratio 3:2
When endpoints are divided into ratios, the formula to calculate the coordinates is;
[tex](x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
Solving for (a): Point C divide AB in ratio 2:3
The ratio;
[tex]m : n = 2 : 3[/tex]
For Point A;
[tex]A(x_1,y_1) = (1,4)[/tex]
For Point B;
[tex]B(x_2,y_2) = (6,-1)[/tex]
Substitute m,n,x1,x2,y1,y2 in the ratio formula given above;
[tex]C(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
[tex]C(x,y) = (\frac{2 * 6 + 3 * 1}{3+2},\frac{2 *-1 + 3 * 4}{3+2})[/tex]
[tex]C(x,y) = (\frac{12 + 3 }{5},\frac{-2 + 12}5})[/tex]
[tex]C(x,y) = (\frac{15 }{5},\frac{10}5})[/tex]
[tex]C(x,y) = (3,2)[/tex]
The coordinates of C is (3,2)
Solving for (b): Point D divide AC in ratio 3:2
Using the same steps as (a) above;
The ratio;
[tex]m : n = 3:2[/tex]
For Point A;
[tex]A(x_1,y_1) = (1,4)[/tex]
For Point C;
[tex]C(x_2,y_2) = (3,2)[/tex]
Substitute m,n,x1,x2,y1,y2 in the folowing ratio formula;
[tex]D(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
[tex]C(x,y) = (\frac{3 * 3 + 2 * 1}{2+3},\frac{3 *2 + 2 * 4}{2+3})[/tex]
[tex]D(x,y) = (\frac{9 + 2}{5},\frac{6 + 8}{5})[/tex]
[tex]D(x,y) = (\frac{11}{5},\frac{14}{5})[/tex]
The coordinates of D is (11/5,14/5)
