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Problem of the Week
Problem B
A Capital Transformation

  1. Plot the given points on the grid, then connect the points in the order they appear in the table. Finish by connecting the last point with the first.

    \(x\) \(y\)
    \(1\) \(10\)
    \(6\) \(10\)
    \(6\) \(9\)
    \(4\) \(9\)
    \(4\) \(5\)
    \(3\) \(5\)
    \(3\) \(9\)
    \(1\) \(9\)

    The coordinate plane with horizontal axis pointing to the right labelled x and vertical axis pointing up labelled y. There are ten horizontal and ten vertical grid lines, each labeled from 1 to 10. A diagonal line is drawn from the origin to the point (10,10).

    2. Reflect each of the points you plotted in part (a) across the diagonal line in the grid above, then connect the reflected points like you did in part (a).

    Tip: When you reflect a point across a line, the reflected point lies on the opposite side of the line, the same perpendicular distance away as the original point. This is shown in the diagram where \(P\) is the original point and \(P^{\prime}\) is its reflection across the diagonal line.

    The coordinate plane with horizontal axis pointing to the right labelled x and vertical axis pointing up labelled y. There are four horizontal and four vertical grid lines, each labeled from 1 to 4. A diagonal line is drawn from the origin to the point (4,4). Point P is at (1,4) and point P prime is at (4,1). A dashed line joins P to P prime and meets the diagonal line at a right angle.

  2. How do the coordinates of each reflected point from part (b) compare with the coordinates of their original point?

  3. Starting with the original points, can you use \(2\) or \(3\) different transformations in a row to get the same final image you drew in part (b)? If so, explain the transformations you used.

Theme: Geometry & Measurement