Question

what are the coordinates of the point $\frac{1}{4}$ of the way from $a(-6, -3)$ to $b(10, 9)$?

Explanation:

Step1: Find the x - coordinate

Use the section - formula for x - coordinate $x=x_1+\frac{k}{1}(x_2 - x_1)$, where $x_1=-6$, $x_2 = 10$ and $k=\frac{1}{4}$.
$x=-6+\frac{1}{4}(10-( - 6))=-6+\frac{1}{4}(10 + 6)=-6+\frac{1}{4}\times16=-6 + 4=-2$

Step2: Find the y - coordinate

Use the section - formula for y - coordinate $y=y_1+\frac{k}{1}(y_2 - y_1)$, where $y_1=-3$, $y_2 = 9$ and $k=\frac{1}{4}$.
$y=-3+\frac{1}{4}(9-( - 3))=-3+\frac{1}{4}(9 + 3)=-3+\frac{1}{4}\times12=-3 + 3=0$

Answer:

$(-2,0)$