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: rise = ____ run = __ slope = ____ problem #3 - unit 2 (mild) identify the slope to the following graph: rise = __ run = __ slope = ______

Explanation:

Problem #1

This problem involves geometric transformations (reflections) of a polygon in the coordinate - plane. Since it is not possible to draw directly in this text - based format, the following are the rules for reflection:

1. Reflection over the y - axis:

• The rule for reflecting a point \((x,y)\) over the y - axis is \((-x,y)\). For each vertex of Polygon A, change the sign of the x - coordinate to get the vertices of Polygon B.

1. Reflection over the x - axis:

• The rule for reflecting a point \((x,y)\) over the x - axis is \((x, - y)\). To get Polygon C from Polygon B, change the sign of the y - coordinate of each vertex of Polygon B.

1. Another reflection over the x - axis:

• To get Polygon D from Polygon C, again change the sign of the y - coordinate of each vertex of Polygon C.

Problem #2

1. Find rise and run:

• Locate two points on the line. Let's say the two points are \((0,4)\) and \((4, - 4)\).
• The rise is the change in the y - values. \(Rise=y_2 - y_1=-4 - 4=-8\).
• The run is the change in the x - values. \(Run=x_2 - x_1=4 - 0 = 4\).

1. Calculate slope:

• The slope \(m\) of a line is given by the formula \(m=\frac{Rise}{Run}\). So, \(m=\frac{-8}{4}=-2\).

Problem #3

1. Find rise and run:

• Let the two points on the line be \((3,4)\) and \((4,-5)\).
• The rise is \(y_2 - y_1=-5 - 4=-9\).
• The run is \(x_2 - x_1=4 - 3 = 1\).

1. Calculate slope:

• Using the slope formula \(m = \frac{Rise}{Run}\), we get \(m=\frac{-9}{1}=-9\).

Answer:

• Problem #1: Follow the reflection rules for drawing.
• Problem #2: \(Rise=-8\), \(Run = 4\), \(Slope=-2\)
• Problem #3: \(Rise=-9\), \(Run = 1\), \(Slope=-9\)