Finding missing coordinates on a graph

A (2,1) B (b,3) C (5,5)

b > 3 and ABC makes a rigt angle trianglem what is b?

I don't just want the answer i would also like the method in how you do it please.

If you plot the points on graph paper you can see b=1 (point(1,3) would make a right triangle.
BUT b must be greater than 3.

So I am going to find the slope of (5,5) and (b,3) then the slope of (2,1),(b,3)
Since I want a right angle (that is perpendicular lines/slopes) I will set their product equal to negative one (def.of slopes of perpendicular lines.)

(5,5),(b,3)
m=(3-5)/(b-5)=(-2)/(b-5)

(2,1),(b,3)
m=(3-1)(b-2)

-2..........2
******x*****..=(-1)
b-5......b-2

........-4.............-1
**************=****
b^2-7b+10.......1

........+4............+1
**************=****
b^2-7b+10.......1

Cross Multiply

b^2-7b+10=4

b^2-7b+6=0

(b-6)(b-1)=0

b=6.....b=1

Since b>3......ANSWER......b=6

I enjoyed this problem....THANKS

If angle ABC is a right angle then AB and BC are perpendicular. This means the product of their gradients is -1.

Gradient AB = (3 - 1)/(b - 2) = 2/(b - 2).
Gradient BC = (5 - 3)/(5 - b) = 2/(5 - b)

Therefore you need to solve 2/(b - 2) * 2/(5 - b) = -1

Can you finish from there?
The quadratic gives you two solutions but the restriction b > 3 eliminates one of them.

what are rigt & trianglem mean?