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The diagram shows triangle A drawn on a grid - Edexcel - GCSE Maths - Question 9 - 2017 - Paper 2
Question 9
The diagram shows triangle A drawn on a grid. Kyle reflects triangle A in the x-axis to get triangle B. He then reflects triangle B in the line y = -x to get triang... show full transcript
Worked Solution & Example Answer:The diagram shows triangle A drawn on a grid - Edexcel - GCSE Maths - Question 9 - 2017 - Paper 2
Step 1
Kyle reflects triangle A in the x-axis to get triangle B
Answer
The reflection of triangle A in the x-axis flips the y-coordinates of its vertices. Suppose the vertices of triangle A are A(x, y), B(x1, y1), and C(x2, y2). After reflection, triangle B will have vertices A'(x, -y), B'(x1, -y1), and C'(x2, -y2).
Step 2
He then reflects triangle B in the line y = -x to get triangle C
Answer
Reflecting triangle B in the line y = -x swaps the x and y coordinates and changes their signs. So, the vertices of triangle C will be A''(-(-y), -x) = A''(y, -x), B''(-(-y1), -x1) = B''(y1, -x1), and C''(-(-y2), -x2) = C''(y2, -x2).
Step 3
Is Amy correct?
Answer
Amy reflects triangle A in the line y = x, resulting in triangle D with vertices A'''(y, x), B'''(y1, x1), C'''(y2, x2). Next, reflecting triangle D in the x-axis changes their positions to A''''(y, -x), B''''(y1, -x1), C''''(y2, -x2).
To determine if triangle E is in the same position as triangle C, we need to compare the coordinates. Triangle C and E are not the same as they have opposite orientations. Hence, Amy is incorrect.