Question

the endpoint of ab are a(-7, -6) and b(5,6) what are the coordinates of point c on ab that is 1/3 the distance from point a to point b

Answer 1

The coordinates of c are (-3,-2)

Explanation:

We have the coordinates of a=(-7,-6) and b=(5,6). We need to find the coordinates of a point c=(x,y) such that:

`d_(ac)=1/3 d_(ab)`

The coordinates x and y have the same relation as the distance:

`x_(ac)=1/3x_(ab)`

Or, equivalently:

`x_a-x=(1)/(3)(x_a-x_b)`

Multiplying by 3:

`3x_a-3x=x_a-x_b`

Operating:

`3x_a-x_a+x_b=3x`

`2x_a+x_b=3x`

Dividing by 3:

`x=(2x_a+x_b)/(3)`

Similarly:

`y=(2y_a+y_b)/(3)`

Substituting:

`x=(2*(-7)+5)/(3)=-3`

`y=(2*(-6)+6)/(3)=-2`

The coordinates of c are (-3,-2)