Question

State true or false:

The points $(1,-1),(5,2)$ and $(9,5)$ are collinear.

• A. True
• B. False

Answer 1

The correct option is A True

Let $P(1,-1),Q(5,2)$ and $R(9,5)$ be the given points

Then
$PQ=\sqrt{(5-1{)}^2+(2+1{)}^2}=\sqrt{16+9}=\sqrt{25}=5$

$QR=\sqrt{(9-5{)}^2+(5-2{)}^2}=\sqrt{16+9}=\sqrt{25}=5$

$PR=\sqrt{(9-1{)}^2+(5+1{)}^2}=\sqrt{64+36}=\sqrt{100}=10$

$\Rightarrow PQ+QR=PR$

$\Rightarrow P,Q,R$ are collinear points