Question

A, B and C are collinear and B is between A and C. The ratio of AB to AC is 1:3. If A is at (2,-6) and B is at (3,-1) what are the coordinates of point C

Answer 1

(5, 9)

Explanation:

The distance between A and B is 1/3 the distance between A and C.

x coordinates:

3 − 2 = 1/3 (x − 2)

1 = 1/3 (x − 2)

3 = x − 2

x = 5

y coordinates:

-1 − (-6) = 1/3 (y − (-6))

5 = 1/3 (y + 6)

15 = y + 6

y = 9

The coordinates of point C are (5, 9).

Answer 2

The coordinate of C is (5,9)

Explanation:

A, B and C are collinear and B is between A and C.

The ratio of AB to AC is 1:3

If A is at (2,-6) and B is at (3,-1)

AB:AC = 1:3

B is between A and C

AB:(AB+BC) = 1:(1+2)

Therefore, AB:BC = 1:2

Let the point C (a,b)

Using section formula:

`x\rightarrow (mx_2+nx_1)/(m+n)`

`y\rightarrow (my_2+ny_1)/(m+n)`

where,

`m\rightarrow 1`

`n\rightarrow 2`

`x_1m\rightarrow 2`

`y_1\rightarrow -6`

`x\rightarrow 3`

`y\rightarrow -1`

Substitute into formula and solve coordinate point C

`3=(1\cdot a+2\cdot 2)/(1+2)`

`3=(a+4)/(3)`

`a=5`

`-1=(1\cdot b-6\cdot 2)/(1+2)`

`-1=(b-12)/(3)`

`b=9`

Hence, The coordinate of C is (5,9)