Question

6 - 19. on graph paper, plot and connect the points to form trapezoid wxyz if its vertices are w(7, 3), x(4, 3), y(1, 9), and z(6, 5). remember that a trapezoid is a 4 - sided figure (quadrilateral) with at least one pair of parallel sides.
a. if wxyz is reflected using the transformation function (x→−x, y→y) to form wxyz, then where is y?
b. name a sequence of at least two rigid transformations that will take wxyz back on to wxyz.
6 - 20. graph the lines y = x + 2 and y = 2x - 1 on the same set of axes. what is their point of intersection?

Explanation:

For 6-19a:

Step1: Apply reflection rule to $Y$

Original $Y$: $(1,9)$. Rule: $(x,y)\to(-x,y)$
Expression: $(-1, 9)$

Rigid transformations preserve shape/size. A reflection over the y-axis reverses the original reflection, or a translation + reflection can also work.

Step1: Set equations equal to each other

To find intersection, solve $x+2=2x-1$

Step2: Solve for $x$

Rearrange terms: $2+1=2x-x$
Expression: $x=3$

Step3: Find $y$ using $y=x+2$

Substitute $x=3$: $y=3+2=5$

Answer:

$Y'$ is at $(-1, 9)$

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For 6-19b: