Lesson 3

Grid Moves

Let’s transform some figures on grids.

Problem 1

Apply each transformation described to Figure A. If you get stuck, try using tracing paper.

A figure A with a point P, a line l and a point P prime on a triangular grid.
  1. A translation which takes \(P\) to \(P’\)
  2. A counterclockwise rotation of A, using center \(P\), of 60 degrees
  3. A reflection of A across line \(\ell\)

Problem 2

Here is triangle \(ABC\) drawn on a grid.

Triangle A B C on a grid. Let (0 comma 0) be the bottom left corner. Then the coordinates of triangle A B C are A(3 comma 8), B(5 comma 7) and C(8 comma 9).

On the grid, draw a rotation of triangle \(ABC\), a translation of triangle \(ABC\), and a reflection of triangle \(ABC\). Describe clearly how each was done.

Problem 3

  1. Draw the translated image of \(ABCDE\) so that vertex \(C\) moves to \(C’\). Tracing paper may be useful.
    Pentagon A B C D E and point C prime. Segment B C is the base of the pentagon and point E is the top. Point C prime is to the right of the pentagon.
  2. Draw the reflected image of Pentagon \(ABCDE\) with line of reflection \(\ell\). Tracing paper may be useful.
    Pentagon \(A\) \(B\) \(C\) \(D\) \(E\) and line \(l\). Segment \(B\) \(C\) is the base of the pentagon and point \(E\) is the top. Line \(L\) is vertical and is to the right of the pentagon.
  3. Draw the rotation of Pentagon \(ABCDE\) around \(C\) clockwise by an angle of 150 degrees. Tracing paper and a protractor may be useful.
    Pentagon A B C D E. Segment B C is the base of the pentagon and point E is the top.
(From Unit 1, Lesson 2.)