Reflections

Here's how to do reflections, step by step.

Here's the problem.

First: Identify the Line you must reflect across.  In this case it's the y-axis, which is the line when all x are zero.

 Next, locate the points on the shape.  Point F is at (3, 5); V (3, 2) and X (5, 2).  Knowing this, you can use the distance from the y-axis to define the next points.  Each point must be the same distance from the line of reflection as its prime (').

So, F' is at (-3, 5); V (-3, 2) and X at (-5,2)  Notice how each point is the same distance away from the y-axis.  F' is 3 away, and F is 3 away too.

Finally draw in your lines.

Misconceptions:

1.  A reflection does not change any of the shapes angles or the lengths of any segments forming the shape.

2.  A reflection is based on a line, not a point.  The line can have any value, not just on the x-axis or y-axis.  Finding the line of reflection is based on how far the points are from each other, then plotting points halfway between until a line is formed.  This means the distance from the two shapes divided by 2.

3.  The shape should not "turn".  It is reflected, not translated and then rotated.

Graphing Linear Equations

Most of you know what a linear equation is.  You've not heard it called this, but you know what it is.  All the sequences we've had so far form linear equations.  So what are some things you can take away from what we've done with sequences?

1.  All linear equations have a constant rate of change.  As in, when x goes up by 1, y goes up by the same number each time, whether it's up by 2, 3, 5, etc.

We call this rate of change m.  In equation form, it's the number that is multiplied by x (remember inverses mean that it could be the number you're dividing by, too!).

These equations also have a constant number where x crosses the y-axis, called the y-intercept.  You find this by setting x to zero.  Then when you multiply by the change, the change falls out, leaving the intercept.  This intercept is called b.

A linear equation has a few different forms, but the most workable form is called the slope-intercept form.  This means we are solving for y by doing stuff to x.  So y = m * x + b

We can then graph the line on a coordinate plane based on using a process table for y = m * x + b.

You can see that demonstrated here: