To work out the scale factor, SF, we need to divide the given side-length on the bigger shape by the corresponding side of the smaller shape. However, in this case we are not given two corresponding sides. Instead we can set an unknown length BE, as x and form the equation, You can use the following table to find the corresponding measure of a mathematically similar shape.

Step 1: Rearrange the linear equation to get one of the unknowns on its own and on one side of the equals sign. begin{aligned} 2x Learn an entire GCSE course for maths, English and science on the most comprehensive online learning Firstly, we will determine the scale factor that relates the side-lengths, dividing the larger by the smaller If we multiply the second equation by 2, we have two equations both with a 2x term, hence subtracting our new equation 2 from equation 1 we get,

Split the transformation up into 2 parts – firstly sketch y=3f(x) which is a stretch vertically by a scale factor of 3 (multiply the y-coordinates by 3: Now we have that the scale factor is \textcolor{blue}{3}, all we need to do to find x is multiply \textcolor{blue}{3} by the length of the corresponding side on the smaller shape. So we get Question 5: The diagram shows two mathematically similar rectangles, ABEF and ACDF. Find the scale factor, giving your answer in surd form. Because one of these equations is quadrati c (Non-linear), we can’t use elimination like before. Instead, we have to use substitution. If we multiply the second equation by 2, we have two equations both with a 2A term, hence subtracting our new equation 2 from equation 1 we get,

If we multiply the first equation by 3, we have two equations both with a 3x term, hence subtracting our new equation 2 from equation 1 we get, b) Now we have the scale factor, we can apply it to the corresponding length to BE which is BC. Hence, we find that, You should have seen some graph transformations before, such as translations and reflections – recall that reflections in the x-axis flip f(x) vertically and reflections in the y-axis flip f(x) horizontally. Here, we will also look at stretches. Two shapes are said to be mathematically similar if all of the angles in the shapes are equal, but the shapes are not necessarily the same size.A level maths revision cards and exam papers for the exam board of your choosing. MME is here to help you study from home with our revision cards and practice papers. The profit from every bundle is reinvested into making free content on MME, which benefits millions of learners across the country. Now, if the scale factor for the side-lengths is \textcolor{red}{4}, then that means that the scale factor for the areas is:

To do this we need to find two corresponding dimensions. For the example below we will use lengths.If we multiply the first equation by 2, we have two equations both with a 2y term, hence adding our new equation 1 and equation 2 we get, Therefore, to find the area of the smaller shape, we need to divide the area of the bigger shape by the area scale factor: 16. Doing so, we get Now, to get the area of the bigger shape, we must multiply the area of the smaller one by this scale factor. Doing so, we get