![]() To do this we must draw on the centre of rotation (2,2) and then draw a line from each vertex to this, then a line of equal length that is in the anticlockwise direction. Rotate the following shape by about the point (2,2) in an anticlockwise direction. Every other part of the rotation is kept the same (the angle and centre of rotation). To find the inverse of a rotation we must simply swap the direction, so for the example above the inverse of a clockwise rotation is anticlockwise. The diagram above shows the rotation of in the clockwise direction about the point (1,2). At the tip of this line is the new point of our shape’s image. ![]() To successfully rotate a shape it is best to draw a line from the centre of rotation to each of the vertices and then draw a line that is the same length but the correct angle and direction from the original. To describe a rotation we need to have three things:ģ) Whether the rotation is clockwise or anticlockwise (the direction) RotationĪ rotation turns a shape about a fixed point by a certain number of degrees. Since we are enlarging about (0,0) we can simply multiply each of the coordinates by the scale factor to give us the new points of the triangle’s image. If you enlarge a triangle with points (12,6), (-10,2) and (6,-4) with a scale factor of 2.5 about the origin (0,0), what would be the new coordinates of the triangle’s image? For example, a point at (-4,3) enlarged with a scale factor 3 would have its corresponding point at (-12,9). A scale factor that is between 0 and 1 would result in an image that is smaller than the original shape.Ī good rule to remember is that if the centre of enlargement is at the points where the x and y axes meet, the point (0,0), then to find the coordinate points of the image we can simply multiply the original shape’s coordinates by the scale factor. We do not always enlarge a shape so that the image is larger than the original. This new shape which we now have is called the image of the original after an enlargement. To find the enlarged shape you need to follow these instructions:ġ) Draw and measure a line from the centre of enlargement to a vertex of the original shape.Ģ) Multiply this length by the scale factor.ģ) Draw a new vertex this distance from the centre of enlargement in the same direction as the original line.Ĥ) Repeat for each vertex and then join up all the new vertices to create a new enlarged shape. To carry out an enlargement we need:īelow is an example of an enlargement with a scale factor of 2 and the dot as the centre of enlargement. As well as this we need the ‘centre of enlargement’ so that we know where the enlargement is done in relation to. The lengths of each side are multiplied by what is called a ‘scale factor’ to get the new shape. The new object will therefore be similar (this means that they have the same angles and sides but are just different sizes). EnlargementĪn enlargement is where we need to change the size of a shape by a certain amount. To do this we must simply reverse the signs of the vector to give us the inverse which is. ![]() So, to find the inverse of any column vectors we must simply change the positives to negatives and vice versa. Therefore, we must simply reverse the signs for the numbers in the column vector so that the shape will be moved back to where it started. Its inverse can also be found this is the column vector which would take the shape back to its original position. The column vector for this translation isĪny movement of an object can be put as a column vector. Here is a picture of a square that has been moved 6 squares to the right and 3 down. The number at the bottom ( y) tells the number an object is moved up or down by, with a positive moving the object up and a negative moving it down. The number on the top ( x) is the left and right movement, with a positive move to the right and negative to the left. This can obviously be up, down, left or right, and a translation written mathematically is as a column vector. TranslationĪ translation is a movement of an object in a straight line. Here we will give a brief description of the main types of transformations. There are many different kinds of transformations and more than one of these can be used on the same object. A transformation is a change in the size or position of an object in relation to something, usually a square background.
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