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
and N
in m:n will be :-
![x=\dfrac{mx_2+nx_1}{m+n}\ ;\ y=\dfrac{my_2+ny_1}{m+n}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7Bmx_2%2Bnx_1%7D%7Bm%2Bn%7D%5C%20%3B%5C%20y%3D%5Cdfrac%7Bmy_2%2Bny_1%7D%7Bm%2Bn%7D)
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}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B2%286%29%2B3%281%29%7D%7B2%2B3%7D%5C%20%3B%5C%20y%3D%5Cdfrac%7B2%28-1%29%2B3%284%29%7D%7B2%2B3%7D)
Simplify,
![\\\\\Rightarrow x=3\ y=2](https://tex.z-dn.net/?f=%5C%5C%5C%5C%5CRightarrow%20x%3D3%5C%20y%3D2)
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}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B3%283%29%2B2%281%29%7D%7B3%2B2%7D%5C%20%3B%5C%20y%3D%5Cdfrac%7B3%282%29%2B2%284%29%7D%7B3%2B2%7D)
Simplify,
![\\\\\Rightarrow x=3\ y=2](https://tex.z-dn.net/?f=%5C%5C%5C%5C%5CRightarrow%20x%3D3%5C%20y%3D2)
Thus , coordinate of D= (2.2,2.8)