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) the slope to the following problem #3 - unit 2 (mild) identify the slope to the graph:

Explanation:

Problem #1:

a.

For a reflection over the y - axis, the rule is $(x,y)\to(-x,y)$. Identify the vertices of Polygon A. Let's assume the vertices of Polygon A are $(x_1,y_1),(x_2,y_2),\cdots$. Then the vertices of Polygon B will be $(-x_1,y_1),(-x_2,y_2),\cdots$. Plot these new vertices to draw Polygon B.

b.

For a reflection over the x - axis, the rule is $(x,y)\to(x, - y)$. Take the vertices of Polygon B (which are already found in part a). Apply the rule to get the vertices of Polygon C. Plot these vertices to draw Polygon C.

c.

Again, for a reflection over the x - axis (using the rule $(x,y)\to(x, - y)$), take the vertices of Polygon C and apply the rule to get the vertices of Polygon D. Plot these vertices to draw Polygon D.

Problem #2 and #3:

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.

Problem #2:

Identify two points on the line in the graph of Problem #2, say $(x_1,y_1)$ and $(x_2,y_2)$. Then calculate $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Problem #3:

Identify two points on the line in the graph of Problem #3, say $(x_1,y_1)$ and $(x_2,y_2)$. Then calculate $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Since we don't have the actual coordinates of the points from the blurry graph for Problem #2 and #3, we can't give numerical answers for the slope. For Problem #1, the actual drawing needs to be done on the coordinate - plane using the rules of reflection as described above.

Answer:

For Problem #1: Follow the steps above to draw Polygon B, C, and D on the coordinate - plane.
For Problem #2: Use the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ with two points on the line from the graph to find the slope.
For Problem #3: Use the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$ with two points on the line from the graph to find the slope.