Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar. The endpoints of AB are A(1,4) and B(6,-1). If point C divides AB in the ratio 2 : 3, the coordinates of point C are (_,_). If point D divides AC in the ratio 3 : 2, the coordinates of point D are (_,_). help plz!

Answer 1

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;

$(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})$

Solving for (a): Point C divide AB in ratio 2:3

The ratio;

$m : n = 2 : 3$

For Point A;

$A(x_1,y_1) = (1,4)$

For Point B;

$B(x_2,y_2) = (6,-1)$

Substitute m,n,x1,x2,y1,y2 in the ratio formula given above;

$C(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})$

$C(x,y) = (\frac{2 * 6 + 3 * 1}{3+2},\frac{2 *-1 + 3 * 4}{3+2})$

$C(x,y) = (\frac{12 + 3 }{5},\frac{-2 + 12}5})$

$C(x,y) = (\frac{15 }{5},\frac{10}5})$

$C(x,y) = (3,2)$

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;

$m : n = 3:2$

For Point A;

$A(x_1,y_1) = (1,4)$

For Point C;

$C(x_2,y_2) = (3,2)$

Substitute m,n,x1,x2,y1,y2 in the folowing ratio formula;

$D(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})$

$C(x,y) = (\frac{3 * 3 + 2 * 1}{2+3},\frac{3 *2 + 2 * 4}{2+3})$

$D(x,y) = (\frac{9 + 2}{5},\frac{6 + 8}{5})$

$D(x,y) = (\frac{11}{5},\frac{14}{5})$

The coordinates of D is (11/5,14/5)