Question

The line segment joining the points $(3,-4)$ and $(1,2)$ is trisected at the points P and Q. If the and co-ordinates of P and Q are $(p,-2)$ and $(\frac{5}{3},q)$ respectively, find the value of p and q.

• A. $p=0$, $q=\frac{7}{3}$
• B. $p=\frac{2}{3}$, $q=\frac{7}{3}$
• C. $p=\frac{7}{3}$, $q=0$
• D. $none$

Answer 1

Answer: (D)

$none$

$letDbemid-pointofABthenmidpointofPQwillbeDtoo.nowco-ordinateofD=\left(\right(\frac{3+1}{2}),(\frac{-4+2}{2}\left)\right)=(2,-1)nowmid-pointofDusingcoordinatesofPandQ=\left(\right(\frac{p+\left(\frac{5}{3}\right)}{2}),(\frac{-2+q}{2}\left)\right)\therefore \left(\frac{p+\left(\frac{5}{3}\right)}{2}\right)=2p=4-\left(\frac{5}{3}\right)=\left(\frac{4}{3}\right)and\left(\frac{-2+q}{2}\right)=-1-2+q=-2q=0$