A workshop moves a template for a medal-ribbon logo, used in school sports day, across a planning grid by the vector \(\binom{2}{-5}\). Triangle \(E\), with...
Question 1 Report
A workshop moves a template for a medal-ribbon logo, used in school sports day, across a planning grid by the vector \(\binom{2}{-5}\). Triangle \(E\), with vertices \((1, 0)\), \((2, 4)\), \((3, 0)\), is set out below.
- Triangle E is mapped using this translation; give the new vertex coordinates. (3)
Answer Details
A translation by the column vector \(\binom{2}{-5}\) means every point of the shape moves 2 units to the right and 5 units down, so \(2\) is added to every \(x\)-coordinate and \(5\) is subtracted from every \(y\)-coordinate. Applying this to each vertex of triangle \(E\): \((1, 0) \to (1+2, 0-5) = (3, -5)\), \((2, 4) \to (2+2, 4-5) = (4, -1)\), and \((3, 0) \to (3+2, 0-5) = (5, -5)\), giving the image vertices \((3, -5)\), \((4, -1)\), \((5, -5)\) [3 marks]. Since a translation preserves both shape and size, the image triangle is congruent to \(E\), simply repositioned lower and to the right.
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