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Triangle A is drawn on the grid below - OCR - GCSE Maths - Question 14 - 2019 - Paper 2
Question 14
Triangle A is drawn on the grid below. (a) Enlarge triangle A with scale factor 3 from the centre of enlargement P. Label the image B. (b) Describe fully the singl... show full transcript
Worked Solution & Example Answer:Triangle A is drawn on the grid below - OCR - GCSE Maths - Question 14 - 2019 - Paper 2
Step 1
Enlarge triangle A with scale factor 3 from the centre of enlargement P.
Answer
To enlarge triangle A with a scale factor of 3 from point P, determine the coordinates of each vertex of triangle A and then apply the enlargement formula:
If the coordinates of a point (x, y) are enlarged from the centre of enlargement (h, k) with a scale factor of k, the new coordinates (x', y') can be found using the formulas:
Thus, for each vertex of triangle A, calculate the coordinates of the corresponding vertex in triangle B and label the resulting triangle as B.
Step 2
Describe fully the single transformation that maps triangle B onto triangle A.
Answer
To map triangle B onto triangle A, a single transformation of 'reduction' needs to be described. Since triangle B is the enlarged version of triangle A, to transform triangle B back to triangle A involves:
A reduction transformation with a scale factor of rac{1}{3} about point P (the centre of enlargement). This means that the coordinates of triangle B will be divided by 3 towards point P, effectively returning it to the dimensions and position of triangle A.