Answer
$$\color {blue}{\bf\text{No, the points are not collinear}}$$
Work Step by Step
For clarity lets start by naming our points:
$A=(0,9)$
$B=(-3,-7)$
$C=(2,19)$
First, we'll use the distance formula for the distance between each pair of points:
$d(P,Q)=\sqrt{(x_{P}-x_{Q})^2+(y_{P}-y_{Q})^2}$
$AB= \sqrt{(0-(-3))^2+(9-(-7))^2}$
$AB= \sqrt{(3^2+16^2}$
$AB= \sqrt{(9+256}$
$AB= \sqrt{265}$
$AC= \sqrt{(0-2)^2+(9-19)^2}$
$AC= \sqrt{(-2)^2+(-10)^2}$
$AC= \sqrt{4+100}$
$AC= \sqrt{400}$
$BC= \sqrt{(-3-2)^2+(-7-19)^2}$
$BC= \sqrt{(-5)^2+(-26)^2}$
$BC= \sqrt{25+676}$
$BC= \sqrt{701}$
Now that we have the lengths of the sides,
$AB=\sqrt{265}$, $AC= \sqrt{400}$, $BC=\sqrt{701}$,
we can see if the two shortest equal the longest.
$\sqrt{265}+ \sqrt{400}=\sqrt{701}$
Which is $\bf \text{false}$, so:
$$\color {blue}{\bf\text{No, the points are not collinear}}$$
