# Test: Transformation Geometry I - Ambitious

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Question 1:   Find the coordinates of $A\left(2,3\right)$ under the translation $\left(\begin{array}{l}-4\\ 5\end{array}\right)$
$\left(-1,7\right)$
$\left(6,-2\right)$
$\left(-8,15\right)$
$\left(-2,8\right)$
Question 2:   Find the coordinates of $A\left(-3,6\right)$ under the translation $\left(\begin{array}{l}7\\ 2\end{array}\right)$
$\left(-10,4\right)$
$\left(6,-3\right)$
$\left(-21,12\right)$
$\left(4,8\right)$
Question 3:   Find the coordinates of the triangle $ABC$ under the translation $\left(\begin{array}{l}3\\ -5\end{array}\right)$

${A}^{\prime }\left(-4,4\right),{B}^{\prime }\left(-1,-4\right),{C}^{\prime }\left(-6,-3\right)$
${A}^{\prime }\left(-1,-1\right),{B}^{\prime }\left(1,2\right),{C}^{\prime }\left(2,-3\right)$
${A}^{\prime }\left(2,-6\right),{B}^{\prime }\left(5,-4\right),{C}^{\prime }\left(0,-3\right)$
${A}^{\prime }\left(-3,5\right),{B}^{\prime }\left(6,-5\right),{C}^{\prime }\left(-9,-10\right)$
Question 4:   Find the coordinates of the triangle $ABC$ under the translation $\left(\begin{array}{l}-7\\ -6\end{array}\right)$

${A}^{\prime }\left(-14,12\right),{B}^{\prime }\left(-42,6\right),{C}^{\prime }\left(-28,-12\right)$
${A}^{\prime }\left(2,0\right),{B}^{\prime }\left(6,1\right),{C}^{\prime }\left(6,2\right)$
${A}^{\prime }\left(-5,-8\right),{B}^{\prime }\left(-1,-7\right),{C}^{\prime }\left(-3,-4\right)$
${A}^{\prime }\left(9,4\right),{B}^{\prime }\left(13,5\right),{C}^{\prime }\left(11,8\right)$
Question 5:   Find the reflection of the triangle $ABC$ across the $x-$ axis

${A}^{\prime }\left(-2,-1\right),{B}^{\prime }\left(-3,4\right),{C}^{\prime }\left(-1,3\right)$
${A}^{\prime }\left(1,-2\right),{B}^{\prime }\left(-4,-3\right),{C}^{\prime }\left(-3,-1\right)$
${A}^{\prime }\left(1,2\right),{B}^{\prime }\left(-4,3\right),{C}^{\prime }\left(-3,1\right)$
${A}^{\prime }\left(-1,2\right),{B}^{\prime }\left(4,3\right),{C}^{\prime }\left(3,1\right)$
Question 6:   Find the reflection of the triangle $ABC$ across the $x-$ axis

${A}^{\prime }\left(2,1\right),{B}^{\prime }\left(-3,-1\right),{C}^{\prime }\left(-2,-3\right)$
${A}^{\prime }\left(2,-1\right),{B}^{\prime }\left(-3,1\right),{C}^{\prime }\left(-2,-3\right)$
${A}^{\prime }\left(1,-2\right),{B}^{\prime }\left(-1,3\right),{C}^{\prime }\left(3,2\right)$
${A}^{\prime }\left(-2,-1\right),{B}^{\prime }\left(3,1\right),{C}^{\prime }\left(2,-3\right)$
Question 7:   Find the reflection of the triangle $ABC$ across the $y-$ axis

${A}^{\prime }\left(-1,-1\right),{B}^{\prime }\left(-3,-2\right),{C}^{\prime }\left(-4,3\right)$
${A}^{\prime }\left(-1,1\right),{B}^{\prime }\left(-2,3\right),{C}^{\prime }\left(3,4\right)$
${A}^{\prime }\left(1,1\right),{B}^{\prime }\left(3,2\right),{C}^{\prime }\left(4,-3\right)$
${A}^{\prime }\left(-1,1\right),{B}^{\prime }\left(-3,2\right),{C}^{\prime }\left(-4,-3\right)$
Question 8:   Find the reflection of the triangle $ABC$ across the $y-$ axis

${A}^{\prime }\left(1,-1\right),{B}^{\prime }\left(-4,-2\right),{C}^{\prime }\left(-1,2\right)$
${A}^{\prime }\left(1,1\right),{B}^{\prime }\left(-4,2\right),{C}^{\prime }\left(-1,-2\right)$
${A}^{\prime }\left(-1,-1\right),{B}^{\prime }\left(-2,4\right),{C}^{\prime }\left(2,1\right)$
${A}^{\prime }\left(-1,1\right),{B}^{\prime }\left(4,2\right),{C}^{\prime }\left(1,-2\right)$
Question 9:   Find the reflection of the triangle $ABC$ across the $y=x$ line

${A}^{\prime }\left(-1,1\right),{B}^{\prime }\left(-2,4\right),{C}^{\prime }\left(1,3\right)$
${A}^{\prime }\left(1,-1\right),{B}^{\prime }\left(2,-4\right),{C}^{\prime }\left(-1,-3\right)$
${A}^{\prime }\left(-1,1\right),{B}^{\prime }\left(-4,2\right),{C}^{\prime }\left(-3,-1\right)$
${A}^{\prime }\left(1,1\right),{B}^{\prime }\left(4,2\right),{C}^{\prime }\left(3,-1\right)$
Question 10:   Find the reflection of the triangle $ABC$ across the $y=x$ line

${A}^{\prime }\left(-2,-3\right),{B}^{\prime }\left(3,1\right),{C}^{\prime }\left(3,-2\right)$
${A}^{\prime }\left(3,-2\right),{B}^{\prime }\left(-1,3\right),{C}^{\prime }\left(2,3\right)$
${A}^{\prime }\left(2,3\right),{B}^{\prime }\left(-3,-1\right),{C}^{\prime }\left(-3,2\right)$
${A}^{\prime }\left(3,2\right),{B}^{\prime }\left(-1,-3\right),{C}^{\prime }\left(2,-3\right)$