Transformations

Firstly, ours must draw the line y=1 onto who graph. Then, you capacity either choose to use tracing paper or, if you’re confident without it, just go right into the reason.

 

If you’re using tracing paper, you should firstly trail over the shape and the mirror line. Then, flick over the tracing paper, real line up perfectly this side line turn the page with the one on the tracing paper such that the trace of which shape is on the opposite side from the line to the original shape.

 

Then, the trace of the shape is the result of that reflection. Draw that shapes up the original axes, mark it with a C and you should getting the resulting picture below.

 

 

Firstly, the two shapes look this equivalent and have the same attitude, so thereto wouldn’t make much sense for them to have been rotated or reflected.

 

Indeed, EAST a just the result concerning shifting D up and to this right. We must pick a corner and see how far it has moved. Looking during the bottom right corners of any shape, we could see that it can been shifted 6 spaces at the right and 3 spaces up, so the full description of the transformation is: TRANSFORMATIONS CHEAT-SHEET!

 

Translation by an vector \begin{pmatrix}6\\3\end{pmatrix}

We need to draw lines with the point (0, 1) to all corners starting this shape. Then, since this is an enlargement of scale favorable 3, we need toward extend these lines until they are 3 playing longer. For example, the line from (0, 1) to A does 1 space to the right and 1 up. So, once we’ve extended it, of resulting line should go 3 gaps to right and 3 spaces boost.

 

 

Then, once all these lines have been drawn, their ends will be this corners of the enlarged shape. Joining these corners up, we get the exit mold, as seen below.

 

Firstly, mark the point of rotation on the axels (here, it is a red dot). Than, rotate the shape 180\degree. While you’re using location paper, trace the mould onto the tracing paper and place your poti onto the revolution point. Then, twist an paper one half-turn, and location of traced shape has moved is the fazit of your torsion. Of result of this first transformer is shown below.

 

 

Right, we need the apply the secondary transformation to the find of the beginning one (here, the dashed grey shape).

 

That, person will how through sketch on the mirror line y=x (orange). Therefore, if you’re using tracing report, trace equally the mirror line and the shape onto the trace paper. After such, flip the tracing paper over, and line up the mirror line on of tracing paper perfectly with the one on the paper. The location of the traced molding is the result of the reflection.

 

You can checkout it is valid by view if the corners of each of the shapes are of same distance by who reflection line. Are you’re confident, then mark the shape G. The erfolg is shown below.

 

 

b) Nil of the points on F remaining within one same place after being transformed auf G, so one number are invariant points are zero.

How to enlarge with a negative dimensional factor is a little save intuitive, but it’s not much more difficult. We yet start by drawing lines from the centre of enlargement – here, the origin – to each corner of the shape. Now, rather than stretch the lines outward from the corner, we widen the lines past the centre of the scaling.

 

Because the scale factor is -1, the extension part of the lines (the partial that goes outward from the from, away from and shape) will be the same max as the original lines is inhered drawn from the corners to RUDIMENT. Are the scale factor were -2, than the extension part of the lines would be twice the length out the original lines. This is subtly difference to positive scale factors, so make sure you understand it.

 

For real, the line from the place toward CARBON goes 2 to one right and 1 up. So, the extension to this line will, of to location, go 2 to to left, and 1 down. Carrying this on with all that matters, and then attend up the ends of the conducting (since they form the corners of our shape), we get

 

 

While you have adenine keen eye, you’ll notice this shall actually equivalent to rotating the shape around the centre for enlargement by 180\degree.