Simplify completely and enter the number that belongs in the green ! math problem in the !

Explanation:

P = (2,4)

P ' = (5, 0) which is found by adding 3 to the x coord of point P and subtracting 4 from the y coord of P

Q = (-3, 2)

Q ' = (0, -2) which is found by adding 3 to the x coord of point Q and subtracting 4 from the y coord of Q

Let's find the slope of the line through points P ' (5,0) and Q ' (0, -2)

m = (y2 - y1)/(x2 - x1)

m = (-2 - 0)/(0-5)

m = -2/(-5)

m = 2/5

The slope of segment P'Q' is 2/5

The slope is the same as the segment PQ. This is because translations (aka shiftings) do not alter the slopes of lines. Think of a camera aimed at the xy axis to look at the line segment PQ. If you slide the camera and keep facing the xy axis, then the segment PQ does not change at all. Therefore it keeps all its properties of being the same length, having the same slope, etc. This is known as an isometry.

Side note: segment PQ is parallel to segment P'Q' as they have the same slope 2/5

abby has a greater debt becasue she owea 5 more then alan does