Activity 1: What's the Same?

Click a grid dot to place each corner of the new figure. One corner at a time.

Answers and teaching notes
  1. 1 — slide along v. Every corner moves right 2 columns and down 1 unit.
  2. 2 — flip over line y. Each corner stays on its own horizontal level and lands the same number of columns on the far side of line y. Corner A is 5 columns from the line, so it goes 5 columns past it.
  3. 3 — flip over line m. Each corner travels at a right angle to m and goes the same distance past it. Countable version: every corner sits on one of the grid lines parallel to m. If d parallel lines separate the corner from m, the image is d columns right and 1½ × d units down. A and F: d = 2. D and E: d = 3. B and C: d = 4.
  4. 4 — slide along w, then flip over line y. Arrow w points the same way as arrow v but is 2½ times as long: right 5 columns, down 2½ units. After the slide, the left edge of the figure lands exactly on line y. Those two corners sit on the mirror, so the flip leaves them fixed and the rest swings across like a hinge.
  5. 5 — how are the images the same? How are they different?
    Same: all four are congruent to S — identical side lengths, angle measures, perimeter, and area. Rigid transformations never change size or shape.
    Different: position, and orientation. Reading the corners A → B → C → D → E → F runs one way around S and the same way around image 1, because a slide preserves orientation. It runs the opposite way around images 2, 3, and 4, because each of those involves one flip. Image 4 uses a slide and a flip, but only one flip, so it is reversed like the others.
  6. Does any point stay fixed? In 1, 2, and 3, no. In 4, the two corners that land on line y after the slide stay put during the flip. A point on the mirror line always maps to itself.