Question

If the points $P(1,4),Q(2,3)andR(-1,6)$ are collinear, then which one is correct.

• A.
  $PQ+PR=QR$
• B.
  $PQ+QR=PR$
• C.
  $PR+QR=PQ$
• D.
  $PR=PQ=QR$

Answer 1

The correct option is A

$PQ+PR=QR$
Let's find the distances PQ,QR and PR using the distance formula.

$PQ=\sqrt{(1-2{)}^2+(4-3{)}^2}=\sqrt{1+1}=\sqrt{2}unitsQR=\sqrt{(2-(-1){)}^2+(3-6{)}^2}=\sqrt{9+9}=\sqrt{18}=\sqrt{9\times 2}=3\sqrt{2}unitsPR=\sqrt{(1-(1){)}^2+(4-6{)}^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}unitsPQ+PR=\sqrt{2}+2\sqrt{2}=3\sqrt{2}units\therefore PQ+PR=QR$

THus, option (a) is correct.