Question

if point (p, q) is $\frac{1}{3}$ of the way from a to b, what are the val
a(-3, -2)
b(12, 4)
p =
, q =

Explanation:

Step1: Use the section - formula for x - coordinate

The section - formula for the x - coordinate of a point that divides the line segment joining $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$ is $x=\frac{mx_2+nx_1}{m + n}$. Here, $m = 1$, $n=2$, $x_1=-3$, and $x_2 = 12$.
$p=\frac{1\times12+2\times(-3)}{1 + 2}$

Step2: Calculate the value of p

$p=\frac{12-6}{3}=\frac{6}{3}=2$

Step3: Use the section - formula for y - coordinate

The section - formula for the y - coordinate of a point that divides the line segment joining $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$ is $y=\frac{my_2+ny_1}{m + n}$. Here, $m = 1$, $n = 2$, $y_1=-2$, and $y_2 = 4$.
$q=\frac{1\times4+2\times(-2)}{1 + 2}$

Step4: Calculate the value of q

$q=\frac{4 - 4}{3}=0$

Answer:

$p = 2$, $q = 0$