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

Answer:

(5, 9)

Step-by-step 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

Answer:

The coordinate of C is (5,9)

Step-by-step 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:

$x\rightarrow \dfrac{mx_2+nx_1}{m+n}$

$y\rightarrow \dfrac{my_2+ny_1}{m+n}$

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

$3=\dfrac{1\cdot a+2\cdot 2}{1+2}$

$3=\dfrac{a+4}{3}$

$a=5$

$-1=\dfrac{1\cdot b-6\cdot 2}{1+2}$

$-1=\dfrac{b-12}{3}$

$b=9$

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