![]() If the reflection of point P(6,2) is P' (6,8), over which line was point P reflected F. ![]() So in this case, what we now know is that negative F of X is a reflection over the X axis. Let's take a moment to reflect on reflections: 4. So no, this this graph flips over the X axis. And if you multiply a positive value by a negative that will become negative. Well, if you were a negative value for Y at first, when you multiply by a negative will become positive. That means all of our why values are going to be the opposite sign. ![]() To reflect a function over the x-axis, multiply it by negative 1 (usually just. If you have a set of coordinates, place a negative sign in front of. So let's say this is our Y equals F of X graph. Reflection Over The X-Axis: Sets of Coordinates. So in other words, if I had a graph, let's just say we had a linear equation. That means we would be taking all of our wide values and making it the opposite sign. Why? So because it's equal to negative Y. So if I go ahead and substitute why in place of F of X, that would give me negative. The original object is called the pre-image, and the reflection is. Similarly, you may ask, what is the rule for a reflection across the X axis When you reflect a point across the line y x, the x-coordinate and y-coordinate change places. A reflection across x-axis is nothing but folding or flipping an object over the x axis. Remember that function notation and F of X is equal to why those are equivalent expressions. The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same. We do that by subtracting $x+1$ from $-1$, to get $x' = -1-(x+1) = -1-x-1 = -2-x$.So in this problem you're being asked to determine if negative F of X is a reflection over the X or the Y axis. (This distance is negative if you are actually to the left of the axis.) Then we need to move to the left by that amount. When the mirror line is the y-axis we change each (x,y) into (x,y) Fold the Paper. When the mirror line is the x-axis we change each (x,y) into (x,y) Y-Axis. The point $x$ is how far to the right of your axis of symmetry? The axis of symmetry has an $x$-coordinate of $-1$, so your distance to the right is $x-(-1)$, or $x+1$. You can try reflecting some shapes about different mirror lines here: How Do I Do It Myself. If you're a perceptive sort, you might notice that the sum of each of these pairs of $x$-coordinates is $-2$, and therefore arrive at the transformation rule $x' = -2-x$, but if not, you can still reconstruct what's happening. Example 2 : Find the image equation of 2x-3y 8 reflected in the y-axis. Put y -y and Original equation > 2x-y+3 0 After reflection > 2x- (-y)+3 0 2x+y+3 0 So, image equation of the given equation is 2x+y+3 0. The point A has Cartesian coordinates (3. If point on a shape is reflected in the line y x : both coordinates change sign (the coordinate becomes negative if it is positive and vice versa) the x-coordinate becomes the y-coordinate and the y-coordinate becomes the x-coordinate. So in each case, the $y$-coordinate stays the same, but $3$ becomes $-5$, $-2$ becomes $0$, $0$ becomes $-2$, and $13$ becomes $-15$. Solution : Required transformation : Reflection about x - axis, So replace y by -y. A shape can be reflected in the line y x. Since it will be a horizontal reflection, where the reflection is over x-3, we first need to determine the. This is a different form of the transformation. A vertical reflection reflects a graph vertically across the. Similar reasoning shows that, for example, Since the line of reflection is no longer the x-axis or the y-axis, we cannot simply negate the x- or y-values. Another transformation that can be applied to a function is a reflection over the x- or y-axis. When you reflect this point, you should end up at the same "height" ($y$-coordinate) of $-5$, but this time four units to the left of your axis of symmetry. (You should follow along and draw things out on a sheet of graph paper or on your computer, in order to make them clear.) Therefore, if you have a point at $(3, -5)$, it is three units to the right of the $y$-axis, but four units to the right of your axis of symmetry. The line $x = -1$ is a vertical line one unit to the left of the $y$-axis. Rather than think about transformation rules symbolically, and trying to generalize them, try thinking about them visually.
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