Why must the compass point be placed on points a and b? how would the construction be different if the compass point were placed at random points on the original line?

The compass point must be placed on points A and B because you need to make arcs which would allow you to make the perpendicular line through the given line. The construction would be different if the compass point were placed at random points on the original line because then the line would not be lined up correctly in the middle and it will not be correct, hence why you need to put the compass on A and B.

Step-by-step explanation: This is what I answered on edg

yes

yes yes yes

step-by-step explanation:

the ratio of red paint to blue paint is always 9/7. that means that, whatever x's value, (4x+12)/(4x-4) has that same ratio. so, set up an equation and cross-multiply to solve for x:

9/7 = (4x+12)/(4x-4)

9(4x-4) = 7(4x+12)

36x - 36 = 28x + 84

8x - 36 = 84

8x = 120

x = 15