Let's quickly review what we already know about reflections in a point
and how the pre-image and image are positioned in relation to one another.

reminder An object and its reflection in a point have the same shape and size. The pre-image has been rotated 180º, and center point, P, is the midpoint of the segments connecting each set of vertices.

The existence of the midpoint of a line segment will be the point reflection's connection to constructions. Let's see how we can put it to work.

If you need additional information on reflections,
go to the lesson on Reflection in a Point.

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bullet Given a figure & a point of reflection, construct the reflected image.

Given: ΔABC and reflection point P in the same plane.
Task: Construct the point reflection of ΔABC and label it ΔA'B'C'

Choose a starting vertex (such as A). Draw a straight line from A through P (extend the line beyond P).
Remember, P is the midpoint of the segment connecting the corresponding vertices.
Measure the length from A to P. Copy this length starting at P and mark off length on the line.
P is now the midpoint and you have located ONE vertex, A', of the image.
This construction is also the construction for a rotation of 180º
about a point.

After repeating this process from each of the three vertices, you will have the vertices of the image ΔA'B'C'.

You have made P the midpoint of all three segments connecting the corresponding vertices.

Done.

The order in which you repeat this process is of no importance.

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bullet Given a figure and its point reflection, construct the center point.

Given: ΔABC and its point reflection ΔA'B'C' through oint P in the same plane.
Task: Construct the center point P.

Choose a starting vertex (such as B). Draw a line segment connecting B to B'.
Remember, P is the midpoint of the segment connecting the corresponding vertices.
Bisect the segment from B to B' to find the midpoint, P. Done.

There is no need to repeat this process for the other vertices, other than to verify your construction.



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