The image shows a right triangle in the coordinate plane. what is the measure of segment ac?

Just use the Pythagorean Theorem. To find the measure of segment AB, just count, or you could use subtraction: point A is on 8, and point B is on 2. 8-2=6 (You should get the same thing is you count.) The other leg, segment BC, is 3 units. (On that one, you could count or use the coordinates on the x axis.) The Pythagorean Theorem says a squared (a^2) + b squared (b^2) = c squared (c^2).
a and b are the legs: 6 and 3, and c is the hypotenuse: segment AC. *Remember when you square something, you multiply it by itself.* So...
6×6=36 (segment AB)
3×3=9 (segment BC)
36+9=45
You're not done yet. 45 is c^2, not segment AC. You have to take the square root of 45, which is 6.7
Segment AC is equal to 6.7