Test solutions with the detailed point scale. Add up your points and spot what to review.
1 Applying the rules / 4 pts
- \((-6 + 7,\; 2 - 5) = (1, -3)\) (1 pt)
- \((6, 2)\) (1 pt)
- \((-6, -2)\) (1 pt)
- \((-y, x) = (-2, -6)\) (1 pt)
2 A half turn / 3 pts
- \((x, y)\to(-x, -y)\): \(K′(-1, -1)\), \(L′(-4, -1)\), \(M′(-1, -3)\). (1.5 pts)
- \(LM^2 = 3^2 + 2^2 = 13\) and \(L′M′^2 = 3^2 + 2^2 = 13\), so \(LM = L′M′ = \sqrt{13}\). (1.5 pts)
3 Composition / 4 pts
- \(T\): \((2, 2)\); then \(R\): \((2, -2)\). (1.5 pts)
- \(R\): \((3, 2)\); then \(T\): \((2, 6)\). (1.5 pts)
- No, \((2, -2)\ne(2, 6)\): the order of a composition matters. (1 pt)
4 Identify the rotation / 3 pts
- \(A(1, 2)\to(-2, 1)\) matches \((x, y)\to(-y, x)\): a \(90^\circ\) counterclockwise rotation. (1 pt)
- \(B(4, 2)\to(-2, 4)\) and \(C(1, 5)\to(-5, 1)\), as given. (1 pt)
- \(270^\circ\) clockwise. (1 pt)
5 Symmetry / 3 pts
- 9 lines (1 pt); \(360^\circ \div 9 = 40^\circ\) (1 pt).
- 2 lines and \(180^\circ\) (1 pt).
6 Congruent triangles / 3 pts
- \(AB = 3\), \(AC = 4\), \(BC = 5\); \(GH = 3\), \(GI = 4\), \(HI = \sqrt{16 + 9} = 5\). The sides match (SSS). (1.5 pts)
- Translate by \(\langle 2, 2\rangle\): \(A\to G\), \(B\to(5, 2)\), \(C\to(2, 6)\). Then rotate \(90^\circ\) counterclockwise about \(G(2, 2)\): \(B\to(2, 5) = H\) and \(C\to(-2, 2) = I\). (1.5 pts)
Test yourself: quick challenge for Grade 10
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