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Answer:
- dashed line slope: -1
- reflection line slope: 1
Explanation:
When an original figure is reflected across a line to make its image, every point on the image is as far from the line as its corresponding original point. The distance from a point to a line is measured perpendicular to the line. This means the line of reflection is the perpendicular bisector of the segment joining a point with its reflected image.
So, if you know the coordinates of a point and its reflected image, you can find the line of reflection as the perpendicular bisector of the segment joining them.
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Consider the upper right dashed line. Its end points are (-6, -1) on the pink figure and (-2, -5) on the blue figure. The slope of the (dashed) segment joining these points is given by the slope formula:
m = (y2 -y1)/(x2 -x1)
For the given coordinates, the slope of the segment is ...
m = (-5 -(-1))/(-2 -(-6)) = -4/4 = -1
The slope of the dashed line is -1.
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The line of reflection is perpendicular to this, so will have a slope that is the opposite reciprocal of -1:
line of reflection slope = -1/m = -1/-1 = 1
The slope of the reflection line is 1.