Question

directions: show all steps of your thinking and circle final answers! problem #1 - unit 1 review (mild) here is polygon a in the coordinate plane: a. draw polygon b, the image of a, using the y - axis as the line of reflection. b. draw polygon c, the image of b, using the x - axis as the line of reflection. c. draw polygon d, the image of c, using the x - axis as the line of reflection. problem #2 - unit 2 (mild) identify the slope to the following graph: problem #3 - unit 2 (mild) identify the slope to the following graph:

Explanation:

Problem #1:

a. Reflection over y - axis

When reflecting a point $(x,y)$ over the y - axis, the transformation rule is $(-x,y)$. Identify the vertices of Polygon A. Let's assume vertices of A are, for example, $(2,2)$, $(4,2)$, $(4,4)$, $(3,4)$. After reflection over the y - axis, the new vertices of Polygon B will be $(-2,2)$, $(-4,2)$, $(-4,4)$, $(-3,4)$. Then draw Polygon B on the coordinate - plane using these new vertices.

b. Reflection over x - axis

When reflecting a point $(x,y)$ over the x - axis, the transformation rule is $(x, - y)$. Take the vertices of Polygon B. If a vertex of B is $(-2,2)$, after reflection over the x - axis, the new vertex of Polygon C is $(-2,-2)$. Do this for all vertices of B and draw Polygon C.

c. Reflection over x - axis again

Using the same rule $(x, - y)$ for reflecting over the x - axis. Take the vertices of Polygon C and find the vertices of Polygon D. For example, if a vertex of C is $(-2,-2)$, after reflection over the x - axis, the new vertex of D is $(-2,2)$. Then draw Polygon D.

Problem #2:

The slope formula is $m=\frac{\text{Rise}}{\text{Run}}$. Given $\text{Rise}=-3$ and $\text{Run}=-2$, then $m = \frac{-3}{-2}=\frac{3}{2}$.

Problem #3:

Given $\text{Rise}=-9$ and $\text{Run}=1$, using the slope formula $m=\frac{\text{Rise}}{\text{Run}}$, we get $m=-9$.

Answer:

Problem #1: Draw Polygon B, C, and D as described above.
Problem #2: $\frac{3}{2}$
Problem #3: $-9$