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 (,).

Answer 1

Answer:  C= (3,2) and D=(2.2, 2.8)

Step-by-step explanation:

The coordinates of point P(x,y) divides a line segment having end points M${x_1,y_1}$ and N$(x_2,y_2)$ in m:n will be :-

$x=\dfrac{mx_2+nx_1}{m+n}\ ;\ y=\dfrac{my_2+ny_1}{m+n}$

Given : 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 will be :-

$x=\dfrac{2(6)+3(1)}{2+3}\ ;\ y=\dfrac{2(-1)+3(4)}{2+3}$

Simplify,

$\\\\\Rightarrow x=3\ y=2$

Thus , coordinate of C= (3,2)

If point D divides AC in the ratio 3 : 2, the coordinates of point D will be :-

$x=\dfrac{3(3)+2(1)}{3+2}\ ;\ y=\dfrac{3(2)+2(4)}{3+2}$

Simplify,

$\\\\\Rightarrow x=3\ y=2$

Thus , coordinate of D= (2.2,2.8)