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Grade 7 · Math · Unit 8 of 10

Coordinates & Transformations

Plot, slide, flip and turn

What your child practises

Reading and plotting points in all four quadrants, and describing translations, reflections, 180° rotations and combinations of them.

Saskatchewan Curriculum outcome: SS7.4, SS7.5 · the Cartesian plane and transformations

How we explain it

Children can open this short lesson before they practise.

  1. A point is (x, y). Go across for x, then up or down for y.
  2. A translation adds or subtracts from x and y.
  3. A reflection in the x-axis changes the sign of y.

Example: Move the point (2, 3) right 4 and down 1. Where does it land? Right 4: x = 2 + 4 = 6. Down 1: y = 3 − 1 = 2. Answer: (6, 2)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    Rectangle ABCD has vertices A(-3, 1), B(3, 1), C(3, -5) and D(-3, -5). What is its area?

    -6-6-5-5-4-4-3-3-2-2-1-100112233445566ABCD

    answer boxsq. units

    Show answer

    36 sq. units

    Hint: Width: 3 − (-3) = 6. Height: 1 − (-5) = 6. Area = 6 × 6 = 36 square units.

  2. Question 2

    What are the coordinates of point A?

    -6-6-5-5-4-4-3-3-2-2-1-100112233445566A
    • (2, 3)
    • (3, 2)
    • (3, -2)
    • (-3, 2)
    Show answer

    (3, 2)

    Hint: Start at the origin (0, 0). Move 3 right along the x-axis, so x = 3. Then move 2 up, so y = 2. Write x first: (3, 2).

  3. Question 3

    Point A(1, 5) is translated 2 units left and 4 units up. What is the x-coordinate of its image, A′?

    answer box

    Show answer

    -1

    Hint: x: 1 − 2 = -1. y: 5 + 4 = 9.

  4. Question 4

    How many units apart are A(-1, -2) and B(5, -2)?

    -6-6-5-5-4-4-3-3-2-2-1-100112233445566AB

    answer boxunits

    Show answer

    6 units

    Hint: They have the same y-coordinate, so count across: 5 − (-1) = 6 units.

  5. Question 5

    Where is the point (-8, 5)?

    • Quadrant I
    • Quadrant II
    • Quadrant III
    • Quadrant IV
    Show answer

    Quadrant II

    Hint: Quadrant I is (+, +), II is (−, +), III is (−, −) and IV is (+, −), going counterclockwise from the top right. A point with a 0 coordinate sits on an axis.

  6. Question 6

    Point P(1, -3) is translated 1 unit right and 2 units down. What are the coordinates of its image, P′?

    -6-6-5-5-4-4-3-3-2-2-1-100112233445566P
    • (2, -1)
    • (0, -1)
    • (2, -5)
    • (-1, -2)
    Show answer

    (2, -5)

    Hint: Right adds to x and left subtracts from x. Up adds to y and down subtracts from y. So P′ = (2, -5).

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