Question

a point p(-5,-5) lies $\frac{1}{2}$ of the way along segment ab from endpoint b(2,9). determine the coordinates of point a.

Explanation:

Step1: Recall mid - point formula

The mid - point formula between two points $A(x_1,y_1)$ and $B(x_2,y_2)$ is $P(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $P(-5,-5)$ is the mid - point of $AB$ with $B(2,9)$. Let the coordinates of $A$ be $(x,y)$.

Step2: Solve for the x - coordinate of A

We know that $\frac{x + 2}{2}=-5$. Cross - multiply: $x + 2=-10$. Then $x=-10 - 2=-12$.

Step3: Solve for the y - coordinate of A

We know that $\frac{y + 9}{2}=-5$. Cross - multiply: $y+9=-10$. Then $y=-10 - 9=-19$.

Answer:

$(-12,-19)$