Answer:
- line of reflection: 1/2
- any dotted line: -2
Explanation:
You want the slopes of the line of reflection and of any dotted line joining a point with its reflected image.
Slope
It works well to find grid intersections where the lines of interest cross them. This makes it easier to count the number of grid squares between points of intersection.
The slope of the solid line of reflection can be determined using the two upper-right open-circle points where the dotted lines cross it. The vertical difference (rise) between those points is 1 grid square. The horizontal difference (run) between those points is 2 grid squares. The slope of the line of reflection is ...
slope = rise/run = 1/2 . . . . . slope of line of reflection
For these differences, rise and run are positive up and to the right.
Dotted lines
There are two ways to find the slope of a dotted line.
1) Use the fact it is perpendicular to the line of reflection, so its slope is the opposite reciprocal of 1/2:
-1/(1/2) = -2 . . . . . slope of dotted line
2) Identify grid points where a dotted line crosses and find the ratio of rise to run.
Using the lower right point on the blue triangle and the open circle at the line of reflection, we see ...
slope = rise/run = -4/+2 = -2 . . . . . slope of dotted line
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