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)

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=(mx_2+nx_1)/(m+n)\ ;\ y=(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=(2(6)+3(1))/(2+3)\ ;\ y=(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=(3(3)+2(1))/(3+2)\ ;\ y=(3(2)+2(4))/(3+2)`

Simplify,

`\\\\\Rightarrow x=3\ y=2`

Thus , coordinate of D= (2.2,2.8)