# Test: Transformation Geometry II - Challenging

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Question 1:   Find the triangle $ABC$ under a reflection across the line $y=-x$, where $A\left(3,-1\right),B\left(-1,3\right),C\left(2,4\right)$:
${A}^{\prime }=\left(1,-3\right),{B}^{\prime }=\left(-3,1\right),{C}^{\prime }=\left(-4,-2\right)$
${A}^{\prime }=\left(3,1\right),{B}^{\prime }=\left(-3,-1\right),{C}^{\prime }=\left(-2,4\right)$
${A}^{\prime }=\left(-3,1\right),{B}^{\prime }=\left(1,3\right),{C}^{\prime }=\left(4,2\right)$
${A}^{\prime }=\left(-3,-1\right),{B}^{\prime }=\left(3,1\right),{C}^{\prime }=\left(2,-4\right)$
Question 2:   Find the triangle $ABC$ under a reflection across the line $y=-x$,  where $A\left(-5,2\right),B\left(-1,3\right),C\left(1,-3\right)$:
${A}^{\prime }=\left(-5,-2\right),{B}^{\prime }=\left(3,-1\right),{C}^{\prime }=\left(-3,-1\right)$
${A}^{\prime }=\left(2,5\right),{B}^{\prime }=\left(-1,-3\right),{C}^{\prime }=\left(1,3\right)$
${A}^{\prime }=\left(-2,5\right),{B}^{\prime }=\left(-3,1\right),{C}^{\prime }=\left(3,-1\right)$
${A}^{\prime }=\left(5,-2\right),{B}^{\prime }=\left(1,-3\right),{C}^{\prime }=\left(1,3\right)$
Question 3:   Find the coordinates of the triangle $ABC$ enlarged by a factor of $2$:
${A}^{\prime }=\left(4,-2\right),{B}^{\prime }=\left(4,-4\right),{C}^{\prime }=\left(2,4\right)$
${A}^{\prime }=\left(-4,-2\right),{B}^{\prime }=\left(-4,-4\right),{C}^{\prime }=\left(-2,4\right)$
${A}^{\prime }=\left(2,-4\right),{B}^{\prime }=\left(-4,4\right),{C}^{\prime }=\left(4,2\right)$
${A}^{\prime }=\left(-4,2\right),{B}^{\prime }=\left(4,4\right),{C}^{\prime }=\left(2,-4\right)$
Question 4:   Find the coordinates of the triangle $ABC$ enlarged by a factor $-\frac{1}{2}$ and centered about the origin:
${A}^{\prime }=\left(-16,4\right),{B}^{\prime }=\left(-8,8\right),{C}^{\prime }=\left(-4,4\right)$
${A}^{\prime }=\left(-4,1\right),{B}^{\prime }=\left(1,-1\right),{C}^{\prime }=\left(-1,1\right)$
${A}^{\prime }=\left(4,-1\right),{B}^{\prime }=\left(2,-2\right),{C}^{\prime }=\left(1,-1\right)$
${A}^{\prime }=\left(-1,4\right),{B}^{\prime }=\left(-2,2\right),{C}^{\prime }=\left(-1,1\right)$
Question 5:   Find the coordinates of the triangle $ABC$ rotated by $90°$ about the origin:
${A}^{\prime }=\left(1,1\right),{B}^{\prime }=\left(3,1\right),{C}^{\prime }=\left(2,4\right)$
${A}^{\prime }=\left(1,2\right),{B}^{\prime }=\left(1,0\right),{C}^{\prime }=\left(4,1\right)$
${A}^{\prime }=\left(1,0\right),{B}^{\prime }=\left(3,0\right),{C}^{\prime }=\left(2,3\right)$
${A}^{\prime }=\left(1,3\right),{B}^{\prime }=\left(1,1\right),{C}^{\prime }=\left(4,2\right)$
Question 6:   Find the coordinates of the triangle $ABC$ rotated by $180°$ about the origin:
${A}^{\prime }=\left(-3,1\right),{B}^{\prime }=\left(-7,-1\right),{C}^{\prime }=\left(-4,-2\right)$
${A}^{\prime }=\left(-3,-1\right),{B}^{\prime }=\left(-7,1\right),{C}^{\prime }=\left(-4,2\right)$
${A}^{\prime }=\left(1,-3\right),{B}^{\prime }=\left(-1,-7\right),{C}^{\prime }=\left(-2,-4\right)$
${A}^{\prime }=\left(-1,3\right),{B}^{\prime }=\left(1,7\right),{C}^{\prime }=\left(2,4\right)$
Question 7:   Find the coordinates of the triangle $ABC$ rotated by $270°$ about the origin:
${A}^{\prime }=\left(-1,1\right),{B}^{\prime }=\left(-3,0\right),{C}^{\prime }=\left(-2,4\right)$
${A}^{\prime }=\left(1,-1\right),{B}^{\prime }=\left(3,0\right),{C}^{\prime }=\left(2,-4\right)$
${A}^{\prime }=\left(1,-1\right),{B}^{\prime }=\left(0,3\right),{C}^{\prime }=\left(-2,-4\right)$
${A}^{\prime }=\left(1,1\right),{B}^{\prime }=\left(3,0\right),{C}^{\prime }=\left(2,4\right)$
Question 8:   Find the coordinates of the triangle $ABC$ rotated by $-90°$ about the origin:
${A}^{\prime }=\left(0,-2\right),{B}^{\prime }=\left(1,-4\right),{C}^{\prime }=\left(-1,-5\right)$
${A}^{\prime }=\left(0,2\right),{B}^{\prime }=\left(1,4\right),{C}^{\prime }=\left(-1,5\right)$
${A}^{\prime }=\left(2,0\right),{B}^{\prime }=\left(4,1\right),{C}^{\prime }=\left(5,-1\right)$
${A}^{\prime }=\left(-2,0\right),{B}^{\prime }=\left(-4,-1\right),{C}^{\prime }=\left(-5,1\right)$
Question 9:   Find the coordinates of the triangle rotated by $90°$ about the origin and enlarged by a factor of $2$:
${A}^{\prime }=\left(2,-2\right),{B}^{\prime }=\left(4,-2\right),{C}^{\prime }=\left(2,-4\right)$
${A}^{\prime }=\left(-1,1\right),{B}^{\prime }=\left(-8,4\right),{C}^{\prime }=\left(-4,8\right)$
${A}^{\prime }=\left(2,2\right),{B}^{\prime }=\left(8,2\right),{C}^{\prime }=\left(2,4\right)$
${A}^{\prime }=\left(2,2\right),{B}^{\prime }=\left(8,4\right),{C}^{\prime }=\left(4,8\right)$
Question 10:   Find the coordinates of the triangle $ABC$ rotated by $180°$ about the origin and enlarged by a factor of $-\frac{1}{3}$:
${A}^{\prime }=\left(-1,2\right),{B}^{\prime }=\left(-2,1\right),{C}^{\prime }=\left(-3,3\right)$
${A}^{\prime }=\left(1,2\right),{B}^{\prime }=\left(2,1\right),{C}^{\prime }=\left(3,3\right)$
${A}^{\prime }=\left(-1,-2\right),{B}^{\prime }=\left(2,2\right),{C}^{\prime }=\left(3,-2\right)$
${A}^{\prime }=\left(2,1\right),{B}^{\prime }=\left(1,2\right),{C}^{\prime }=\left(3,3\right)$