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

Answer:

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

Step-by-step 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:

$x_a-x=\frac{1}{3}(x_a-x_b)$

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:

$x=\frac{2x_a+x_b}{3}$

Similarly:

$y=\frac{2y_a+y_b}{3}$

Substituting:

$x=\frac{2*(-7)+5}{3}=-3$

$y=\frac{2*(-6)+6}{3}=-2$

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