Question

The line segment joining the points $(1,-2)$ and $(-3,4)$ is trisected at the points $P$ and $Q$. Find the coordinates of the point $P$ and $Q$.

Answer 1

We are given with line segment joining the points $A(1,-2),B(-3,4).$

$P$ and $Q$ are the points of trisection of $AB$ that is $AP=PQ=QB.$

Therefore, $P$ divides $AB$ internally in the ratio $1:2.$

So, the coordinates of $P$, by applying the section formula, are

$(\frac{1(-3)+2\left(1\right)}{1+2},\frac{1\left(4\right)+2(-2)}{1+2})$

$\Rightarrow (\frac{–1}{3},0)$

Now, $Q$ divides $AB$ internally in the ratio $2:1$. So, the coordinates of $Q$ by applying section formula are,

$(\frac{2(-3)+1\left(1\right)}{1+2},\frac{2\left(4\right)+1(-2)}{1+2})$

$\Rightarrow (\frac{–5}{3},\frac{4}{3})$

Therefore, the coordinates of the points of trisection of the line segment joining $A$ and $B$ are

$P(\frac{–1}{3},0),Q(\frac{–5}{3},\frac{4}{3})$