Find the coordinates of the points of trisection of the line segment joining $(4,-1)$ and $(-2,-3)$.
Step-by-Step Solution
Key Concept: The two trisection points divide the segment in ratios 1:2 and 2:1 respectively.
First trisection point $P$ (ratio $1:2$ from $A$): $P=\left(\dfrac{1(-2)+2(4)}{3},\dfrac{1(-3)+2(-1)}{3}\right)=\left(2,-\dfrac53\right)$. [1.5 Marks]
Second trisection point $Q$ (ratio $2:1$ from $A$): $Q=\left(\dfrac{2(-2)+1(4)}{3},\dfrac{2(-3)+1(-1)}{3}\right)=\left(0,-\dfrac73\right)$. [1.5 Marks]
Correct Answer: