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Math 7

Math 7 · Worksheets

Constructions and transformations

Ten questions of mixed difficulty, covering Geometry. Print it, or work through it on screen — the answer key starts on its own page.

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Constructions and transformations

Math 7 · maddyhelps.com

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Circle the best answer for each question. Show your work in the space provided.

  1. The point (2, 5) is translated 3 units right and 4 units down. Where does it end up?

    1. a) (−1, 9)
    2. b) (6, 2)
    3. c) (5, 9)
    4. d) (5, 1)

  2. The perpendicular bisector of a line segment

    1. a) runs beside it and never meets it
    2. b) cuts it into two equal parts, at any angle
    3. c) crosses it at a right angle, at any point
    4. d) crosses it at its midpoint, at a right angle

  3. The point (3, −2) is rotated 180° about the origin. What is its image?

    1. a) (3, 2)
    2. b) (−3, 2)
    3. c) (2, 3)
    4. d) (−3, −2)

  4. The point (4, 1) is rotated 90° counterclockwise about the origin. What is its image?

    1. a) (−1, 4)
    2. b) (−4, −1)
    3. c) (1, −4)
    4. d) (1, 4)

  5. Point P is in quadrant III. It is 3 units from the x-axis and 5 units from the y-axis. What are its coordinates?

    1. a) (−3, −5)
    2. b) (5, 3)
    3. c) (−5, −3)
    4. d) (−5, 3)

  6. In which quadrant is the point (−3, 5)?

    1. a) quadrant III
    2. b) quadrant IV
    3. c) quadrant I
    4. d) quadrant II

  7. A rectangle has corners at (−3, 2), (4, 2), (4, −1) and (−3, −1). What is its perimeter?

    1. a) 8 units
    2. b) 21 units
    3. c) 20 units
    4. d) 16 units

  8. The point (4, −3) is reflected in the x-axis. What is its image?

    1. a) (−3, 4)
    2. b) (4, 3)
    3. c) (−4, 3)
    4. d) (−4, −3)

  9. After a translation, the point A(1, 2) has moved to A′(−3, 5). Which translation was it?

    1. a) 4 units right and 3 units down
    2. b) 2 units left and 3 units up
    3. c) 4 units left and 3 units up
    4. d) 3 units left and 5 units up

  10. You fold a sheet of paper so that point A lands exactly on point B, then unfold it. What is the fold line?

    1. a) a line parallel to segment AB
    2. b) the straight line that joins point A to point B
    3. c) a line through A, perpendicular to segment AB
    4. d) the perpendicular bisector of segment AB

Answer key · Constructions and transformations

Math 7 · maddyhelps.com

  1. d) (5, 1) — Right adds to the x-coordinate and down subtracts from the y-coordinate: (2 + 3, 5 − 4) = (5, 1). (5, 9) moves up instead of down, and (6, 2) puts the 4 on x and the 3 on y.
  2. d) crosses it at its midpoint, at a right angle — The name has two parts: perpendicular means it meets the segment at 90°, and bisector means it cuts the segment into two equal halves. A line that does only one of these is not a perpendicular bisector, and a line that never meets the segment is parallel to it.
  3. b) (−3, 2) — A half turn about the origin carries a point to the opposite side of the origin, so both coordinates change sign: (−3, 2). (3, 2) and (−3, −2) change only one sign — those are reflections in an axis — and (2, 3) is only a quarter turn.
  4. a) (−1, 4) — A quarter turn counterclockwise carries a point to the right of the origin round to above it, so (4, 1) in quadrant I lands in quadrant II at (−1, 4): the coordinates swap and the new x-coordinate is negative. (1, −4) is the clockwise quarter turn, and (−4, −1) is a half turn.
  5. c) (−5, −3) — How far a point is from the x-axis is how far up or down it is, which is its y-coordinate; how far it is from the y-axis is its x-coordinate. In quadrant III both are negative, so P is (−5, −3). (−3, −5) matches each distance to the axis it names, which puts the numbers the wrong way round.
  6. d) quadrant II — A negative x-coordinate is left of the y-axis and a positive y-coordinate is above the x-axis, so the point is in the top-left quadrant. The quadrants are numbered counterclockwise from the top right — I, II, III, IV — so top left is quadrant II.
  7. c) 20 units — From x = −3 to x = 4 is 7 units (3 to reach the y-axis and 4 more), and from y = −1 to y = 2 is 3 units, so the perimeter is 7 + 3 + 7 + 3 = 20 units. Taking 3 from 4 gives a width of 1 and a perimeter of 8 — count across the axis, not the gap between the digits. 21 is the area.
  8. b) (4, 3) — Reflecting in the x-axis flips the point to the other side of that axis, so the x-coordinate stays the same and the y-coordinate changes sign: (4, 3). (−4, −3) is the reflection in the y-axis, the most common mix-up.
  9. c) 4 units left and 3 units up — Compare the new coordinates with the old ones: x goes from 1 to −3, a change of −4, which is 4 left, and y goes from 2 to 5, which is 3 up. Subtracting the other way round gives 4 right and 3 down, and 3 left and 5 up reads the image's coordinates as the move.
  10. d) the perpendicular bisector of segment AB — The fold sends A onto B, so every point on the crease is the same distance from A as from B, and the crease crosses AB at its midpoint at a right angle — exactly a perpendicular bisector. It cannot pass through A, because A lands on B, not on itself.