Combination-Of-Transformations Wjec-Eduqas Higher

Combination of transformations

What do I need to know about combined transformations?

• Combined transformations are when more than one transformation is performed, one after the other

• In many cases, two transformations can be equivalent to one alternative single transformation

  • Finding this single transformation is a common exam question

• Rotation

  • Requires an angle, direction and centre of rotation

  • It is usually easy to tell the angle from the orientation of the image

  • You can use trial and error and tracing paper to find the centre of enlargement

• Reflection

  • A reflection will be in a mirror line which can be vertical (x = k), horizontal (y = k) or diagonal (y = mx + c)

  • Points on the mirror line do not move

  • It is possible for a mirror line to pass through the object

• Translation

  • A translation is a movement which does not change the orientation or size of the shape, it simply moves location

  • A translation is described by a vector in the form 

    • This represents a movement of x units to the right and y units vertically upwards

What are common combinations of transformations?

• A combination of two reflections can be the same as a single rotation

  • One reflection using the line and the other using the line 

  • This is the same as a 180° rotation about the centre <img alt=”open parentheses a comma space b close parentheses” data-mathml='<math ><semantics><mfenced><mrow><mi>a</mi><mo>,</mo><mo>&#160;</mo><mi>b</mi></mrow></mfenced><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true}</annotation></semantics></math>’ height=”22″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2222%22%20width%3D%2241%22%20wrs%3Abaseline%3D%2216%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfenced%3E%3Cmrow%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E%2C%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmi%3Eb%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A’math1f7177163c833dff4b38fc8d287’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAADRjdnQgDVUNBwAAAVAAAAA6Z2x5ZoPi2VsAAAGMAAAAUmhlYWQQC2qxAAAB4AAAADZoaGVhCGsXSAAAAhgAAAAkaG10eE2rRkcAAAI8AAAACGxvY2EAHTwYAAACRAAAAAxtYXhwBT0FPgAAAlAAAAAgbmFtZaBxlY4AAAJwAAABn3Bvc3QB9wD6AAAEEAAAACBwcmVwa1uragAABDAAAAAUAAADSwGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAg1UADev96AAAD6ACWAAAAAAACAAEAAQAAABQAAwABAAAAFAAEACAAAAAEAAQAAQAAACz%2F%2FwAAACz%2F%2F%2F%2FVAAEAAAAAAAABVAMsAIABAABWACoCWAIeAQ4BLAIsAFoBgAKAAKAA1ACAAAAAAAAAACsAVQCAAKsA1QEAASsABwAAAAIAVQAAAwADqwADAAcAADMRIRElIREhVQKr%2FasCAP4AA6v8VVUDAAABAFX%2FZADVAIAACgAAMzUzFRQGByc%2BATdVgC8vGx4eAYB6PVEUKQ40MQAAAAEAAAABAADVeM5BXw889QADBAD%2F%2F%2F%2F%2F1joTc%2F%2F%2F%2F%2F%2FWOhNzAAD%2FIASAA6sAAAAKAAIAAQAAAAAAAQAAA%2Bj%2FagAAF3AAAP%2B2BIAAAQAAAAAAAAAAAAAAAAAAAAIDUgBVATMAVQAAAAAAAAAoAAAAUgABAAAAAgBeAAUAAAAAAAIAgAQAAAAAAAQAAN4AAAAAAAAAFQECAAAAAAAAAAEAEgAAAAAAAAAAAAIADgASAAAAAAAAAAMAMAAgAAAAAAAAAAQAEgBQAAAAAAAAAAUAFgBiAAAAAAAAAAYACQB4AAAAAAAAAAgAHACBAA