Lesson 5

Coordinate Moves

Let’s transform some figures and see what happens to the coordinates of points.

Problem 1

  1. Here are some points.
    Points \(A\), \(B\) and \(C\) on a coordinate plane, origin \(O\).

    What are the coordinates of \(A\), \(B\), and \(C\) after a translation to the right by 4 units and up 1 unit? Plot these points on the grid, and label them \(A’\), \(B’\) and \(C’\).

  2. Here are some points.
    Points \(D\), \(E\) and \(F\) on a coordinate plane, origin \(O\).

    What are the coordinates of \(D\), \(E\), and \(F\) after a reflection over the \(y\) axis? Plot these points on the grid, and label them \(D’\), \(E’\) and \(F’\).

  3. Here are some points.
    Points \(G\), \(H\) and \(I\) on a coordinate plane, origin \(O\).

    What are the coordinates of \(G\), \(H\), and \(I\) after a rotation about \((0,0)\) by 90 degrees clockwise? Plot these points on the grid, and label them \(G’\), \(H’\) and \(I’\).

Problem 2

Describe a sequence of transformations that takes trapezoid A to trapezoid B.

Quadrilateral A and its image quadrilateral B are trapezoids.
(From Unit 1, Lesson 4.)

Problem 3

Reflect polygon \(P\) using line \(\ell\).

Polygon P and dashed line \(l\) on a grid.
(From Unit 1, Lesson 3.)