MATH Integrated Math II  - Unit 3: The Coordinate Plane and Line Segments
Graphing Points in Quadrant I

State the term that matches the given description for the first six questions.

1) the components of an ordered pair

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2) a pair of numbers that represent a location on a grid

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3) the point where the x-axis and the y-axis intersect in the coordinate plane

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4) a numbered grid system that has a horizontal number line and a vertical number line that are perpendicular to each other and meet at the origin

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5) the four regions of the coordinate plane

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6) the plural of axis

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Graphing Points in Quadrants II, III, and IV

7) In the figure below, determine the coordinates of each of the named points. (a) What are the coordinates of point A? (b) What are the coordinates of point B? (c) What are the coordinates of point C? (d) What are the coordinates of point D? (e) What are the coordinates of point E? (f) What are the coordinates of point F?

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A rectangle is shown in the figure below. The upper right vertex is located at (6, 8) and the lower left vertex is located at (–10, –4). Based on the given points, determine the ordered pairs for points A, B, C, D, E, and F, and then answer the next two questions.

8) Answer the following questions: (a) What are the coordinates of point A? (b) What are the coordinates of point B? (c) What are the coordinates of point C?

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9) Answer the following questions: (a) What are the coordinates of point D? (b) What are the coordinates of point E? (c) What are the coordinates of point F?

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10) A rectangle is plotted in the coordinate plane. The vertices (corners) of the rectangle are given as A(–2,3), B(4,3); C(–2, –2) and D(x,y). What is the ordered pair for point D?

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Refer to the figure below to answer the next four questions. In this set of questions, you will be guided in making two translations of the rectangular figure. When a figure is translated, it is moved to another location on the grid. You may want to print this picture before beginning the exercise. (Right-click on the figure and select “Print Picture”.)

11) Write the ordered pairs for point P, point Q, point S, and point R. Write the letter, and then the ordered pair. For example: P(1,2).

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Activity: Translate Rectangle PQRS by moving the rectangle 3 units to the left and two units down. (This means to move each of the vertices of the rectangle 3 units to the left and two units down, and then redraw the rectangle.) Name this rectangle P’Q’R’S’. (Note P’Q’R’S’ is a way to denote a new rectangle translated from an original rectangle and is read P-primed, Q-primed, R-primed, S-primed.)

12) What are the coordinates of the vertices of the new rectangle’s location? (When stating the ordered pairs of each vertex, use the new notation for the points. Example: use P’ to denote the upper left vertex of the new rectangle).

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Activity: Translate Rectangle P’Q’R’S’ by moving this rectangle 4 units to the right and one unit up. Denote the new rectangle as P’’Q’’R’’S’’. (This notation is used to denote that the figure has been translated a second time and is read P double-primed, Q double-primed, R double-primed, S double-primed.)

13) What are the coordinates of the vertices of the new rectangle (P”Q”R”S”)?

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14) Describe the translation that would occur if rectangle PQRS was moved DIRECTLY to rectangle P’’Q’’R’’S’’ (in other words, no middle step)?

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Ruler Postulate and Segment Addition

State the term that matches the given description for the next three questions.

15) line segments that measure the same length

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16) a number's distance from zero on the number line

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17) In mathematics, the symbol below represents what?

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Refer to the figure below to answer the next four questions.

18) What is the length of segment EB?

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19) What is the length of segment AD?

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20) What is the length of segment GB?

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21) State two segments that are congruent to segment FB.

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22) Use the figure below to help solve the following problem: The length of segment TV is 75 and point U is a point on segment TV between points T and V. What are the lengths of segments TU and UV if the length of segment TU is “4x – 10” and the length of segment UV is “2x + 7”? Check your answers to make sure the length of the two segments total the length of TV (75).

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23) Draw a figure to solve the following problem: Segments PO and OM are located on line PM. Point O is between points P and M. The length of segment PM is 110. What are the lengths of segments PO and OM if the length of segment PO is “7y +12” and the length of segment OM is “3y – 8”? Check your answers.

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24) Refer to the figure below to solve the following problem: Point E is a point on segment DF between points D and F. The length of segment EF is 6. What are the lengths of segments DE and DF if the length of segment DE is “5x +13” and the length of segment DF is “7x -25”? Check your answers.

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