Slide 1
Reflections on Coordinate Grids
The vertices of the pre-image and the corresponding vertices in the mirror image are equidistant from the reflection line. To see why this is true, let’s look at this reflection, where the triangle is reflected over the x-axis.
Point A in the pre-image is 3 units from the x-axis, which is the reflection line.
Point A prime in the mirror image is also 3 units from the reflection line.
Point C in the pre-image is 2 units from the reflection line.
Point C prime in the mirror image is also 2 units from the reflection line.
Point B in the pre-image is 7 units from the reflection line.
Point B prime in the mirror image is also 7 units from the reflection line.
Image Description: A four quadrant grid with the x-axis extending from negative ten to ten, and the y axis extending from negative eight to eight. Triangle ABC is graphed with point A at (negative five, three), point B at (negative three, seven), and point C (negative two, two). Triangle ABC is reflected over the x axis. The x axis is marked as the reflection line. The image of the reflection is triangle A prime B prime C prime. It is plotted such that point A prime is at (negative five, negative three), point B prime is at (negative three, negative seven), and point C prime is at (negative two, negative two).
Slide 2
Reflect the triangle over the y-axis.
Drag and drop the reflected triangle on the right of the screen to the appropriate location on the coordinate grid.
Description of Work Area: There are two sections. On the left is a four quadrant grid with the x-axis extending from negative eight to eight and the y-axis extending from negative eight to eight. Triangle DEF is plotted with point D at (negative six, zero), point E at (negative one, three), and point F (negative two, negative five). The y-axis is marked as the reflection line.
On the right is the Reflected Triangle identified as Triangle D prime E prime F prime. This triangle will be the image of Triangle DEF when it is reflected over the reflection line. This triangle is to be dragged to the coordinate grid to accurately show the reflection.
Slide 3
Reflect the triangle over the x-axis.
Drag and drop the reflected triangle on the right of the screen to the appropriate location on the coordinate grid.
Description of Work Area: There are two sections. On the left is a four quadrant grid with the x-axis extending from negative eight to eight and the y-axis extending from negative eight to eight. Triangle GHI is plotted with point G at (negative one, one), point H at (two, seven), and point I at (six, three). The x-axis is marked as the reflection line.
On the right is the Reflected Triangle identified as Triangle G prime H prime I prime. This triangle will be the image of Triangle GHI when it is reflected over the reflection line. This triangle is to be dragged to the coordinate grid to accurately show the reflection.
Slide 4
Reflect the triangle over the y = x line.
Drag and drop the reflected triangle on the right of the screen to the appropriate location on the coordinate grid.
Notice that the reflection line is y = x.
Description of Work Area: There are two sections. On the left is a four quadrant grid with the x-axis extending from negative ten to ten and the y-axis extending from negative eight to eight. Triangle BCD is plotted with point B at (one, four), point C at (negative two, seven), and point D at (negative three, three). The line y equals x is marked as the reflection line.
On the right is the Reflected Triangle identified as Triangle B prime C prime D prime. This triangle will be the image of Triangle BCD when it is reflected over the reflection line. This triangle is to be dragged to the coordinate grid to accurately show the reflection.
Slide 5
Let’s take a closer look at reflecting images over the axes. Shown below are triangles that have been reflected over the x-axis. Pay attention to the coordinates of the vertices.
Description of Quiz area:
On the left is a four quadrant grid with the x-axis extending from negative ten to ten and the y-axis extending from negative eight to eight. Triangle ABC is plotted so that point A is at (one, six). Point B is at (two, two), and point C is at (four, four). The x-axis is the reflection line. The reflected image is triangle A prime B prime C prime. Point A prime is at (one, negative six). Point B prime is at (two, negative two), point C is at (four, negative four).
On the right is a four quadrant grid with the x-axis extending from negative ten to ten and the y-axis extending from negative eight to eight. Triangle PQR is plotted with point P at (negative seven, negative seven), point Q is at (two, negative four), and point R is at (one, zero). The x-axis is the reflection line. The reflected image is triangle P prime Q prime R, where P prime is at (negative seven, seven), Point Q prime is at (two, four), and Point R remains at (one, zero).
Which rule describes the transformation of the coordinates for a reflection over the x-axis?
There are four answer choices provided.
The correct answer is B.
Slide 6
Now, explore reflections over the y-axis.
Description of Quiz area:
On the left is a four quadrant grid with the x-axis extending from negative ten to ten and the y-axis extending from negative eight to eight. Triangle MNO is plotted with point M at (negative nine, two), point N at (negative nine, six), and point O at (negative two, two). The y-axis is the reflection line. The reflected image is triangle M prime N prime O prime with Point M prime at (nine, two), point N prime at (nine, six), and point O prime at (two, two).
On the right is a four quadrant grid with the x-axis extending from negative ten to ten and the y-axis extending from negative eight to eight. Triangle XYZ is plotted with point X at negative (ten, seven), point Y at (one, one), and point Z at (negative seven, negative six). The y-axis is the reflection line. The reflected image is triangle X prime, Y prime Z prime, with X prime at (ten, seven), Y prime at (negative one, one) and Z prime at (seven, negative six).
Which rule describes the transformation of the coordinates for a reflection over the y-axis?
There are four answer choices provided.
The correct answer is A.
Slide 7
Here are some reflections over the y = x line.
Description of Quiz area:
On the left is a four quadrant grid with the x-axis extending from negative ten to ten and the y-axis extending from negative eight to eight. Triangle XYZ is plotted with point X at (three, negative two), point Y at (three, negative seven), and Point Z at (six, negative four). The line y equals x is the reflection line. The reflected image is triangle X prime Y prime Z prime, with X prime at (negative two, three), Y prime at (negative seven, three), and Z prime at (negative four, six).
On the right is a four quadrant grid with the x-axis extending from negative ten to ten and the y-axis extending from negative eight to eight. Triangle ABC is plotted with point A at (zero, negative three), point B at (three, three), and Point C at (five, zero). The line y equals x is the reflection line. The reflected image is triangle A prime B C prime, with A prime at (negative three, zero), B remains at (three, three), and C prime at (zero, five).
Which rule describes the transformation of the coordinates for a reflection over the y = x line?
There are four answer choices provided.
The correct answer is C.
Slide 8
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