We are given two figures that are the image of each other. The first part asks us what is the measure of the following angles:
[tex]m\measuredangle SCS^{\prime}=m\measuredangle TCT^{\prime}=m\measuredangle UCU^{\prime}[/tex]
Since these angles are all part of straight lines, this means that their measure is 180 degrees.
Part B. We are asked to determine the length of segments CS and CS' which have the same measure. Therefore, we can obtain the measure of CS only. To do that we will use the Pythagorean theorem since this segment forms a right triangle with the x and y axes. The segment CS is the hypothenuse, therefore, its length is:
[tex]CS^2=(-5)^2+(7)^2[/tex]
Solving the squares we get:
[tex]CS^2=25+49[/tex]
Now we add the results:
[tex]CS^2=74[/tex]
Now we take the square root:
[tex]CS=\sqrt[]{74}=8.6[/tex]
Therefore the length of the segments is 8.6 units.
The same procedure can be used for the other segments.
Part C. We notice that all angles that are formed by a point and its image with a vertex at the center of rotation are equal to 180 degrees. This was proved in part A. Also, all the points and their corresponding images are at the same distance of the center of rotation, this was proved in part B. Therefore, the right statements are the third ones. age are
