If segment CD has endpoints (–3, 4) and (5, 2), what are the coordinates of its midpoint?
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The x-coordinates of will be the negation of the x-coordinates of
The line segment from S to the y-axis equals the line segment from S' to the y-axis. Similarly, the line segment from T to the y-axis equals the line segment from T' to the y-axis
See attachment for and
In order to solve this question, I will make the following assumptions.
Assume that the coordinates of are
Refer to attachment for illustrations
<u>(1) Reflect </u><u> over y-axis and describe the transformation</u>
To reflect across the y-axis, the following rule must be followed
This means that:
<u>The description of the </u><u>transformation </u><u>is as follows:</u>
Notice that the signs of the x-coordinates and
of both triangles are different.
In other words, if the x-coordinate of one is positive, then the other will have a negative x-coordinate; and vice versa.
<u>(2) Compare the segments and the line of reflection</u>
To reflect across the y-axis means that the reflecting line is the y-axis, itself.
The distance between a point to the y-axis is the absolute value of the x-coordinate.
So, the distance between S and the y-axis is:
The distance between S' and the y-axis is:
We can conclude that the two line segments are equal.
This is the same for other point T and T' because of the formula used above.
<u>From T and T' to the y-axis is:</u>
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