Little by little: March 2014

Sunday, 2 March 2014

12.5 Drawing a locus

A locus is a set of points that follow a given rule. The plural of locus is loci. You would need a ruler and compass to draw loci accurately.

If you are asked to draw locus of points that are all 4cm from a point, that means you have to draw a circle with a radius of 4cm.

If you are asked to draw locus of points that are 3cm from a given line, that means you have to draw 2 parallel lines with the distance of 3cm to the given line.

mathcaptain.com

If you are asked to draw locus of points that are 4cm of a given line segment, that means you have to draw 2 parallel lines and semicircle at the right side and left side of the line. The shape would be like this:

ncetm.org.uk

That's the end of this session. Thank you!

Saturday, 1 March 2014

12.4 Enlarging Shapes

When you enlarge a shape, all the lengths of the shape increase in the same proportion. This is called a scale factor. All the angles in the same shape stay in the same size.

When you describe an enlargement you must give: the scale factor of the enlargement and the position of centre of enlargement.

Here is the example of enlarging shape:

12.3 Transforming Shapes

You can use a combination of translations, reflections and rotations to transform a shape.

You can also describe the transformation that maps an object onto its image.

To describe a reflection you must give: the equation of the mirror line.
To describe a translation you must give: the column vector.
To describe a rotation you must give: the centre of rotation (CP), the number of degrees of the rotation and the direction of the rotation.

12.2 Solving Transformations Problems

Under the three transformations (translation, rotation, reflection) an object and its image are always congruent.

When you reflect a shape on a coordinate grid you have to know the equation of the mirror line. Mirror line is a line that will reflect a shape in front, rear, left, right.

This also important for you to remember:
All vertical lines are parallel to the y-axis and have the equation X = 'a number'
All horizontal lines are parallel to the x-axis and have the equation Y = 'a number'

Here is the example:

When you rotate a shape on a coordinate grid you need to know the coordinates of the centre points, size of haw many degree it turns and the direction whether it's clockwise or anti-clockwise.

When you translate a shape on a coordinate grid, you can describe its movement with a column vector.

This is an example of column vector

The top number states how many units to move the shape right (positive number) or left (negative number).

The bottom number states how many units to move the shape up (positive number) or down (negative number).

For example:

means 'move the shape 2 units left (because it's negative) and 3 units up.

12.1 Tesselating Shapes

A tessellation is a pattern made of identical shapes. You can make your own tesselation by fitting copies of a shape together, without gaps or overlaps.

Here are some ecamples of shape that tessellate with themselves.

gwydir.demon.co.id

euler.slu.edu

geom.uiuc.edu

You can see that coopies of a shape fits together without any gaps to make a tessellation.

In any tessellations, the sum of the angles at the point where the vertices of the shapes meet is 360 degree. Keep it in your mind that id there are gaps between the shapes that fits together or if the sum of angles won't be 360 degree, it means that is not tessellating shapes.

12 Tessellations, Transformations and Loci

Hello for everyone. This chapter 12 of Cambridge Checkpoint Mathematics discuss about tessellations, transformations, and loci. So first, let me introduce you translation, rotation and reflection briefly by giving you some examples.

Translation