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


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

  1. What is the shape of quadrilateral ? Justifyyour 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.

    On coordinate grid, trapezoid, W Z Y X, with blue dashed horizontal & vertical segments between points, W & Z, red dashed horizontal & vertical segments between points, Z & Y, purple dashed horizontal segments between points, Y & X.

  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 consists of , 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!

    Close up of vertex x at (3, comma 4) & the origin, interior of 6 enclosed sided polygon is shaded yellow, starting at the point (0, comma 4), going right 3, down 4, right 1, down 3, left 4, & up 7 to enclose the polygon.

    See how the yellow rectangle has rotated clockwise?


    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: 6-67 HW eTool