zMath 180  - Unit 21: Transformations
By following instructions given through coordinate transformations, the location or size of figures may change in the coordinate plane. The changes are described by stating how each of the coordinates of the ordered pairs should be replaced.

For example, the phrase “replace (x, y) with (x, –y)” means to plot new points where the x-coordinates remain the same but the y-coordinates are changed to the opposite. Thus, point P(3, –2) would be replaced with new point P'(3, 2). (Note: P' is read P-primed.)

For the first six problems, print out the graph paper provided in the content area titled “Graph Paper 1”. Complete the sketches of each transformation about Pentagon PQRST described in the first six problems, and then answer the corresponding questions.

1) Replace (x, y) with (x, –y). What kind of transformation occurs?

2) Replace (x, y) with (–x, y). What kind of transformation occurs?

3) Replace (x, y) with (–x, –y). What kind of transformation occurs?

4) Replace (x, y) with (y, –x). What kind of transformation occurs?

5) To achieve a rotation of the figure by 90 degrees in a counterclockwise direction, replace (x, y) with:

6) Enlarge the figure by a scale factor of 2. List the name of each of the new vertices of the dilated figure along with the corresponding new ordered pairs.

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7) Which translation would move pentagon PQRST to the new location to create pentagon P'Q'R'S'T'?

For the next six problems, print out the graph paper titled “Graph Paper 2” provided in the content area. Complete the following activity: Draw a triangle with vertices at (1,2), (1,6), (5,2) in each of the six coordinate planes provided on the graph paper. Then, complete each of the transformations in the next six problems and draw a new triangle. State the vertices of the image.

8) Translate the triangle right three units, then down one unit. What are the coordinates of the image?

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9) Reflect the triangle over the y-axis. What are the coordinates of the image?

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10) Reflect the triangle over the x-axis. What are the coordinates of the image?

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11) Rotate the triangle 180 degrees counterclockwise. What are the coordinates of the image?

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12) Rotate the triangle 90 degrees clockwise. What are the coordinates of the image? (The first ordered pair would be (2, –1). As you find the other two ordered pairs, you should be able to draw a 90 degree angle from the original point to the transformed point with the origin being the vertex of the right angle.)

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13) How would the area of a triangle be affected if the base and height are dilated by 1/2? An example may be used in the explanation. (Hint: Recall that the area of a triangle may be found by using the following formula: A = (1/2)bh.)

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For the next two problems, print out one sheet of the graph paper titled “Graph Paper 2” provided in the content area. Complete the following activity: Draw a square with vertices at (1,1), (1,5), (5,1), (5,5) in each of two of the coordinate planes provided on the graph paper. Then, complete the transformations in the next two problems and draw a new square.

14) Translate the square right one unit, then down two units. What are the coordinates of the image?

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15) Translate the square left two units, then up three. What are the coordinates of the image?

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Review

Label all answers for problems that use measurements of units such as centimeter (cm), millimeter (mm), square centimeter (sq cm), cubic centimeter (cu cm), miles per hour (mph), etc.

Draw a sketch of the similarity based on the given facts, and then answer the next three questions.

16) What is the length of FD?

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17) What angle is congruent to angle D?

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18) What angle is congruent to angle B?

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19) The rate in which a river flows is measured in miles per hour. If a boat travels at a speed of 15 miles per hour down stream and reaches its destination sooner than expected, explain what effect the current had on the rate of the boat.

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20) What is the circumference of a circle with a radius of eight centimeters? Express the answer in hundredths.

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21) Find the measure of an exterior angle of a regular pentagon.

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22) Use a proportion and the conversion factor from the chart below to determine the number of inches in 100 centimeters.

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23) Calculate the square root to the nearest tenth.

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In the next seven problems, line “k” and line “l” are parallel lines cut by transversal “m”.

24) Name all angles congruent to angle 1.

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25) Name all angles congruent to angle 2.

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26) Name one pair of vertical angles.

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27) Name one pair of corresponding angles.

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28) Name one pair of alternate interior angles.

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29) Name a pair of supplementary angles.

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30) Alternate EXTERIOR angles are angles located on the exterior of the parallel lines and on opposite sides of the transversal. Is a pair of alternate exterior angles supplementary angles or congruent angles?

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31) Find the sum.

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32) Find the difference

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33) What is 25% of 250?

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34) What is 10% of 1000?

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35) What is the surface area of a square prism that measures 4 centimeters by 4 centimeters by 6 centimeters?

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36) What is volume of a square prism that measures 4 centimeters by 4 centimeters by 6 centimeters?

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37) What is the surface area of a square pyramid that has a base that measures 5 centimeters by 5 centimeters and has a slant height that measures 8 centimeters?

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38) What is the volume of a square pyramid that has a base that measures 3 centimeters by 3 centimeters and has a height that measures 6 centimeters?

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39) Thirty-five percent of Erin’s dance class is under the age of 12. There are 200 dancers in her class. How many dancers are 12 or older?

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40) For the previous problem, would it be an obvious mistake to assume that the answer was more than 200 dancers? Please explain.

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41) Find the missing ordered pair of a square that has the three given vertices.

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42) Find the missing ordered pair of a square that has the three given vertices.

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43) Find the missing ordered pair of an isosceles right triangle that has the two given vertices.

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44) Solve for “x” using inverse operations.

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45) State the letter of the graph that represents the solution to the given inequality.

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