Find the equation of the line that passes through the points (1,1) and (3,5)

To find the equation of the line that passes through the given points, you first must find the slope using the slope intercept formula (y2-y1)/(x2-x1) which is used by plugging your coordinate values into the formula. This would look like this:
(5-1)/(3-1)

When simplified, you should get 4/2 or (when simplified) 2 as your slope.
Now that you have this, you can plug in one of your coordinates and your slope into y=mx+b to solve for b. Since I am using the coordinate (1,1), the equation would look like this: 1=2(1)+b
When solved for b, you should get b=-1

Finally, now that you have the b and m (slope) values, you can write your equation as y=2x-1

A’b’c’ are the coordinates to the new location of the transformed triangle abc. find the distance between the coordinates points to use for your calculations.