Question

#1.) graph the following equations:
x = 5
**y = -6
#2.) the diagram abcd below is graphed below. perform the following transformations by writing your mapping, graphing the line of reflection, then graphing and labelling the image:
a) **efgh is the image of abcd. graph and label the coordinates of efgh after ( r_{x = 0} ).
b) what is a possible line of reflection that would result in all points of the image having negative x values and positive y values?
#3.) two points are graphed below.
a.) state the coordinates of the image of ( (3,2) ) after a reflection across the line ( y = x ). name this point c.
b.) **state the coordinates of the image of ( (-5,6) ) after a reflection across the line ( x = -4 ). name this point d.

Explanation:

#1

For \(x = 5\)

Step1: Identify the type of line

The equation \(x=5\) is a vertical line. For any vertical line \(x = a\), all points on the line have an \(x\) - coordinate equal to \(a\) and \(y\) can be any real number.

Step2: Plot the line

On the coordinate plane, draw a straight vertical line passing through the point \((5,0)\). Points on this line include \((5,1)\), \((5, - 2)\), \((5,3)\) etc.

For \(y=-6\)

Step1: Identify the type of line

The equation \(y =-6\) is a horizontal line. For any horizontal line \(y = b\), all points on the line have a \(y\) - coordinate equal to \(b\) and \(x\) can be any real number.

Step2: Plot the line

On the coordinate plane, draw a straight horizontal line passing through the point \((0,-6)\). Points on this line include \((1,-6)\), \((-2,-6)\), \((3,-6)\) etc.

#3

a)

Step1: Use the reflection rule

The rule for reflecting a point \((x,y)\) across the line \(y = x\) is \((x,y)\to(y,x)\).

Step2: Apply the rule

For the point \((3,2)\), when we apply the rule \((x,y)\to(y,x)\), we get \((2,3)\)

Step1: Use the reflection rule

The rule for reflecting a point \((x,y)\) across the line \(x = a\) is \((x,y)\to(2a - x,y)\). Here \(a=-4\).

Step2: Apply the rule

For the point \((-5,6)\), substitute \(x=-5\) and \(a =-4\) into the formula \(x'=2a - x\). Then \(x'=2\times(-4)-(-5)=-8 + 5=-3\), and \(y'=y = 6\)

Answer:

The coordinates of point \(C\) are \((2,3)\)

b)