Question

find the coordinates of the point 1/3 of the way from a to b. a(-3,-2) b(12,4) coordinates = ( )

Explanation:

Step1: Calculate x - coordinate

Use the section - formula for x - coordinate $x=\frac{(1 - r)x_1+rx_2}{1}$, where $r = \frac{1}{3}$, $x_1=-3$, $x_2 = 12$.
\[x=(1-\frac{1}{3})(-3)+\frac{1}{3}(12)=\frac{2}{3}\times(-3) + 4=-2 + 4=2\]

Step2: Calculate y - coordinate

Use the section - formula for y - coordinate $y=\frac{(1 - r)y_1+ry_2}{1}$, where $r=\frac{1}{3}$, $y_1=-2$, $y_2 = 4$.
\[y=(1-\frac{1}{3})(-2)+\frac{1}{3}(4)=\frac{2}{3}\times(-2)+\frac{4}{3}=\frac{-4 + 4}{3}=0\]

Answer:

$(2,0)$