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Home > CCG > Chapter 6 > Lesson 6.2.2 > Problem 6-67

6-67.

On graph paper, plot and connect the points to form quadrilateral if , , , and .

  1. What is the shape of quadrilateral ? Justify your conclusion.

    Quadrilateral looks like a trapezoid, but make sure by comparing the slopes of the sides that look parallel.

  2. Find the perimeter of quadrilateral .

    Find the lengths of the sides that are not parallel to an axis by drawing slope triangles and using the Pythagorean Theorem.

  3. If quadrilateral is reflected using the transformation function (, ) to form quadrilateral , then where is ?

    Reflect the points across the -axis by finding the distance between the point and axis and placing the reflected point that number of units to the other side of the axis.

    Since is at and a -axis reflection then only the -coordinate should change.
    should be plotted at .

    Repeat this process for the other points!
    Where should be reflected to?

    Plot it and name it .
    Keep going with the other points.

  4. Rotate quadrilateral about the origin clockwise to form quadrilateral . What is the slope of ?

    You may find it helpful to rotate points by drawing a rectangle between the origin and the point and then rotating the rectangle clockwise.
    Keep your eye on the point you're actually working on!

    See how the yellow rectangle has rotated clockwise?

    So

    This slope can be written as .

    Use the eTool below to solve the parts of the problem.
    Click the link at right for the full version of the eTool: CCG 6-67 HW eTool (Desmos)