(3,3),(-1,2),(4,-5) reflect over y=-3

Answer 1

The line y = -3 is a horizontal line that we will be flipping over. This means it will be similar to an x-axis reflection (which is equivalent to flipping over y=0) where the y coordinate is the one that is being changed. However, the method is slightly different. We must figure out how far each point is from the line y=-3, then create the same change but on the opposite side of the line.

Steps:

1.Find the change in y for each point.

Change in y = y-coordinate - y of line of reflection

2 Find the opposite change

3.Add the opposite change to the y of the line of reflection to create the new y coordinate

4.Create new coordinate pair

First point: (3,3)

Change in y = 3 - (-3) = +6

The point (3,3) is +6 above the line y=-3, so the reflected point will be -6 below the line y=-3

New y coordinate: -3 + -6 = -9

New coordinate pair = (3,-9)

Second point: (-1,2)

Change in y = 2- (-3) = +5

This point is +5 above the line so the reflected point will be -5 below the line

New y coordinate: -3 + -5 = -8

New coordinate pair = (-1,-8)

Third point: (4,-5)

Change in y = -5 - (-3) = -2

This point is -2 under the line so the reflected point will be +2 above the line

New y coordinate: -3 + 2 = -1

New coordinate pair = (4,-1)

Answer 2

Hi Jorge R.,

For each point (there are 3 points, you do each one separately), leave the given x-value unchanged; from your given y-value (3, for the first point) go to -3 and then the same distance on the OTHER side of y = -3. So you went from 3 to -3, that's 6 units, and then continued 6 more units on the other side of y = -3, that's to y = -9, isn't it. So the reflected point is (3, -9).

And so on, for the other points.

Note that you can reflect a point across a line (y = -3, for example, or x = 20, for example), across a point ( (3, 4) for example) or across a plane in 3-D. That last one is a little trickier, you will need to get familiar with expressions for planes and how to determine perpendiculars. That's a little more complicated than for a point and a line!

-- Cheers, -- Mr. d.