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The graph of the curve C with equation $y = f(x)$ is transformed to give the graph of the curve S with equation $y = -(x-1) - 3$ - Edexcel - GCSE Maths - Question 15 - 2019 - Paper 3

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The-graph-of-the-curve-C-with-equation--$y-=-f(x)$-is-transformed-to-give-the-graph-of-the-curve-S-with-equation--$y-=--(x-1)---3$-Edexcel-GCSE Maths-Question 15-2019-Paper 3.png

The graph of the curve C with equation $y = f(x)$ is transformed to give the graph of the curve S with equation $y = -(x-1) - 3$. The point on C with coordinates ... show full transcript

Worked Solution & Example Answer:The graph of the curve C with equation $y = f(x)$ is transformed to give the graph of the curve S with equation $y = -(x-1) - 3$ - Edexcel - GCSE Maths - Question 15 - 2019 - Paper 3

Step 1

Find the transformation

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Answer

The graph of curve C is transformed into curve S through the following transformations: a reflection over the x-axis and a translation to the right by 1 unit, followed by a downward shift of 3 units.

Step 2

Apply the transformations to the point (7, 2)

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Answer

  1. Reflection Over the x-axis: The new y-coordinate becomes −2-2. Therefore, the point transforms to (7, -2).

  2. Translation Right by 1: The new x-coordinate becomes 7+1=87 + 1 = 8. So now the point is (8, -2).

  3. Downward Shift by 3: The new y-coordinate becomes −2−3=−5-2 - 3 = -5. Therefore the final coordinates become (8, -5).

Step 3

State the coordinates of Q

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Answer

Thus, the coordinates of Q are (8, -5).

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