Reflections: description to algebraic rule
At about 86s and 99s the narrator says the "x-axis" becomes the opposite when he means the x-coordinate. An on-screen note corrects this.
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Quadrilateral ABCD is reflected over the y-axis. Point A(-3, 8) becomes A'(3, 8): the y-coordinate stays the same and the x-coordinate becomes its opposite, so the rule is (x, y) -> (-x, y). The rule is then used to predict B'(7, 6) from B(-7, 6).
You'll be able to
- reflect a point over the y-axis.
- write the rule (x, y) -> (-x, y) for a reflection over the y-axis.
- use a rule to predict image points without the graph.
Key words
- reflection
- A flip of a shape over a line so it becomes a mirror image.
- y-axis
- The vertical number line on a coordinate grid.
- equidistant
- The same distance away; a point and its reflection are equidistant from the mirror line.
- opposite
- The same number with the other sign, like -7 and 7.
Transcript
- [Instructor] We are told that Amelia reflected quadrilateral ABCD, we could see it right over here, over the y-axis, ` so it's gonna be reflected over the y-axis, to create quadrilateral A'B'C'D', which they haven't showed us. Write a rule that describes this transformation.
So pause this video and have a go at this, before we do this together. Well, let's just think about what this transformation will do to the different points on this quadrilateral. We could start with point A. Point A right now, is at the coordinates (- 3,8). (-3,8).
Let's think about what happens after this transformation. This transformation, we are going to reflect over the y-axis. So if A is right over here, if it's three units to the left of the y-axis here, then after the reflection, A', which is right over here, is gonna be three units to the right.
It's gonna have the same y-coordinate, but it's x-coordinate is going to become the opposite. So we can see it is now at the point (3,8). (3,8) and this is point A'. That's in the image right over there. And so you might already be seeing a pattern. The y-coordinate will stay the same, we saw that with that eight, but we are flipping over the y-axis, so the x-axis becomes the opposite.
So already I have a good candidate rule here that if whatever (x,y) I start with in the pre-image, that's going to become, the y-coordinate is going to be the same, but the x-axis is going to become the opposite. And we could try that with more points if we like.
For example, we could go to B. B has coordinates (-7,6) right now, (-7,6). And now without even looking at this, I'm gonna cover my eyes while I still write on the right side. If I just apply this rule over here, this rule would predict, alright, let's take the opposite of the x-coordinate, which would now be positive seven and use the same y-coordinate, which is six.
So let's see, (7,6) (7,6), looks exactly right for B'. We have the same height, the same y-coordinate, and we are equidistant from the y-axis but now we have flipped over to the other side, so we had an x-coordinate of negative seven. Now it is positive seven.
And you could verify that with the other coordinates as well if you're interested. And you're gonna see that it completely flips that quadrilateral over the y-axis.
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