zMath 180
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Unit 20: Using Coordinate Geometry
1) Find the missing ordered pair of a rectangle that has the three given vertices.
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2) Find the missing ordered pair of a rectangle that has the three given vertices.
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3) Find the missing ordered pair of a square that has the three given vertices.
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4) Find the missing ordered pair of an isosceles right triangle that has the two given vertices.
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Print out the figure below and determine where a fourth point T could be placed to make a parallelogram, and then answer the next three questions. (Note: Three different parallelograms can be formed depending on which quadrant point T is placed.)
5) Name the coordinates of point T, when placed in Quadrant I, that makes parallelogram QRST.
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6) Name the coordinates of point T, when placed in Quadrant II, that makes parallelogram QRTS.
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7) Name the coordinates of point T, when placed in Quadrant III, that makes parallelogram QTRS.
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8) Where would point T be placed in Quadrant I to make trapezoid QRST such that the non-parallel sides are congruent? State the coordinates of point T.
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9) Determine the area of the trapezoid in the previous problem. [Hint: A = (1/2)h(a + b)]
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10) Determine the area of the outer ring (red) of the circle. (a) What is the area of the outer ring? (b) Give an explanation of how to solve the problem.
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Refer to the drawing of a pair of parallel lines cut by a transversal to answer the next six problems.
11) List four pairs of vertical angles and write them as congruence statements. (Example: Angle 9 is congruent to angle 10.)
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12) List four pairs of corresponding angles and write them as congruence statements.
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13) List four pairs of angles that are supplementary
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14) List two pairs of alternate interior angles and write them as congruence statements.
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15) List four acute angles.
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16) List four obtuse angles.
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For the next seven problems, find the surface area or the volume. Label the answers correctly with square units or cubic units, whichever is appropriate.
17) Surface area of a square pyramid: base is 2 cm x 2 cm, slant height is 3 cm.
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18) Surface area of a cube: base edge is 4.2 cm
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19) Volume of a square prism: base area is 14 sq cm, height is 18 cm.
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20) Volume of a cylinder: base area is 14.1 sq cm; height is 16 cm.
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21) Volume of a triangular prism: base area is 14 sq cm; height is 10 cm.
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22) Volume of a cylinder: radius of 4 cm, height of 6 cm.
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23) Volume of a cone: radius of 4 cm, height of 6 cm.
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24) What is the perimeter of a square with an edge length of 3.5 centimeters?
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25) What is the perimeter of a rectangle that has a base of 4.2 centimeters and a height of 5.2 centimeters?
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26) What is the measure of an interior angle of a regular decagon?
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27) What is the measure of the exterior angle of a regular decagon?
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For the next two problems, refer to the chart below to convert the given measurements.
28) 10 pounds (lb) = ________ kilograms (kg) (Round the answer to the nearest tenth.)
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29) 3000 millimeters (mm) = __________ inches (in)
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30) Find the square root.
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31) Find the square root.
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32) Find the square root.
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33) Find the square root.
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34) Write the number in standard form.
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35) Write the number in standard form.
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36) On paper, draw the net for a cylinder. Describe the drawing by stating the names of the shapes and stating the number of each different shape.
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37) On paper, draw a net for a square pyramid on paper. Describe the drawing by stating the names of the shapes and stating the number of each different shape.
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38) Explain how a net helps when finding the surface area of a solid?
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39) A rectangular solid is built by stacking 1 x 1 x 1 cubes as shown in the figure. What is the total number of 1 x 1 squares that cover the six faces (surfaces) of the rectangular solid?
a.) 120
b.) 112
c.) 196
d.) 144
40) How many 1 x 1 x 1 cubes would it take to build the solid in the previous problem?
a.) 120
b.) 112
c.) 196
d.) 144
41) The cubes that are within the solid are white and not painted. How many 1 x 1 x 1 white cubes (sides all white) are inside the solid?
a.) 20
b.) 28
c.) 50
d.) 10
42) Which graph represents the solution to the given inequality? State the letter of the correct graph.
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