Question

Point A is at (-2,4) and point C is at (4,7). Find the coordinates of point B on AC such that the ratio of a B to a C is 1:3

Answer 1

(0,5)

Explanation:

Ratio of lengths

Take coordinates

4-(-2)=6

AC:6

AB: 2

BC:4

7-4=3

AC=3

AB=1

BC=2

B: (-2+2,4+1)

(0,5)

Answer 2

`[x=(1(4)+3(-2))/(1+3), y=(1(7)+3(4))/(1+3)]`

`[x=(4-6)/(4), y=(7+12)/(4)]`

`[x=(-2)/(4), y=(19)/(4)]`

`[x=-0.5, y=4.75]`

Therefore, the coordinates of point 'b' would be (-0.5 , 4.75).

Explanation:

We have been given that point a is at (-2,4) and point c is at (4,7) .

We are asked to find the coordinates of point b on segment ac such that the ratio is 1:3.

We will use section formula to solve our given problem.

When point P divides a segment internally in the ratio m:n, the coordinates of point P would be:

`[x=(mx_2+nx_1)/(m+n), y=(my_2+ny_1)/(m+n)]`

`\texttt{Let point} (-2,4)=(x_1,y_1) \texttt {and point} (4,7)=(x_2,y_2).`

`[x=(1(4)+3(-2))/(1+3), y=(1(7)+3(4))/(1+3)]`

`[x=(4-6)/(4), y=(7+12)/(4)]`

`[x=(-2)/(4), y=(19)/(4)]`

`[x=-0.5, y=4.75]`

Therefore, the coordinates of point 'b' would be (-0.5 , 4.75).