There are two ways. It will be instructive to learn
both methods.

Find the length of AB by drawing this blue
right triangle with AB as its hypotenuse: 



The bottom leg of the blue triangle is obviously 7 units long.
(The bottom leg looks purple since it's blue over a red x-axis).
You can just count them. And the right leg of the blue triangle 
is obviously 4 units tall.  You can tell by looking at the units 
of the y axis.

Now AB is the hypotenuse of the blue right triangle. So we use
the Pythagorean theorem:






Now we erase the blue right triangle and draw a
green one:

We find the length of AC by drawing this green
right triangle with AC as its hypotenuse:

 

The bottom leg of the green triangle is obviously 8 units long.
And the right leg of the green triangle is obviously 1 unit tall.

Now AC is the hypotenuse of the green right triangle. So we use
the Pythagorean theorem:






So the lengths of AB and AC are both equal to.
Therefore triangle ABC is isosceles.

HERE'S THE SECOND WAY;

Use the distance formula to find AB:








Use the distance formula to find AC:








So the lengths of AB and AC are both equal to.
Therefore triangle ABC is isosceles.

Edwin