# Test: Transformation Geometry I - Challenging

Double click on maths expressions to zoom
Question 1:   Write down the coordinates of $\left(\begin{array}{l}2\\ -2\end{array}\right)$ under the translation $\left(\begin{array}{l}-3\\ 7\end{array}\right)$
$\left(\begin{array}{l}-6\\ -14\end{array}\right)$
$\left(\begin{array}{l}5\\ 9\end{array}\right)$
$\left(\begin{array}{l}-5\\ -9\end{array}\right)$
$\left(\begin{array}{l}-1\\ 5\end{array}\right)$
Question 2:   Write down the coordinates of $\left(\begin{array}{l}0\\ 7\end{array}\right)$ under the translation $\left(\begin{array}{l}2\\ -8\end{array}\right)$
$\left(\begin{array}{l}0\\ 1\end{array}\right)$
$\left(\begin{array}{l}-2\\ 15\end{array}\right)$
$\left(\begin{array}{l}2\\ -1\end{array}\right)$
$\left(\begin{array}{l}0\\ -56\end{array}\right)$
Question 3:   Write down the coordinates of the triangle $ABC$ under the translation $\left(\begin{array}{l}-5\\ -7\end{array}\right)$, where $A=\left(3,2\right),B=\left(6,5\right),C=\left(7,1\right)$
$A\text{'}=\left(8,9\right),B\text{'}=\left(11,12\right),C\text{'}=\left(12,8\right)$
$A\text{'}=\left(-15,-14\right),B\text{'}=\left(-30,-35\right),C\text{'}=\left(-35,-7\right)$
$A\text{'}=\left(-2,-5\right),B\text{'}=\left(1,-2\right),C\text{'}=\left(2,-6\right)$
$A\text{'}=\left(-4,-3\right),B\text{'}=\left(-1,0\right),C\text{'}=\left(-4,0\right)$
Question 4:   Write down the coordinates of the triangle $ABC$ under the translation $\left(\begin{array}{l}6\\ -4\end{array}\right)$, where $A=\left(-2,-1\right),B=\left(1,4\right),C=\left(2,0\right)$
$A\text{'}=\left(-4,-4\right),B\text{'}=\left(0,7\right),C\text{'}=\left(-4,8\right)$
$A\text{'}=\left(-5,4\right),B\text{'}=\left(-7,0\right),C\text{'}=\left(-4,8\right)$
$A\text{'}=\left(4,-5\right),B\text{'}=\left(7,0\right),C\text{'}=\left(8,-4\right)$
$A\text{'}=\left(-12,4\right),B\text{'}=\left(6,-16\right),C\text{'}=\left(12,0\right)$
Question 5:   Find the triangle $ABC$ under a reflection in the $x$-axis, where $A=\left(-4,2\right),B=\left(-2,5\right),C=\left(-1,-1\right)$
$A\text{'}=\left(-4,-2\right),B\text{'}=\left(-2,-5\right),C\text{'}=\left(-1,-1\right)$
$A\text{'}=\left(4,2\right),B\text{'}=\left(2,-5\right),C\text{'}=\left(-1,1\right)$
$A\text{'}=\left(-4,2\right),B\text{'}=\left(-2,5\right),C\text{'}=\left(1,1\right)$
$A\text{'}=\left(4,-2\right),B\text{'}=\left(2,-5\right),C\text{'}=\left(1,-1\right)$
Question 6:   Find the triangle $ABC$ under a reflection in the $x$-axis, where $A=\left(-2,-1\right),B=\left(-1,5\right),C=\left(3,2\right)$
$A\text{'}=\left(-2,1\right),B\text{'}=\left(-1,-5\right),C\text{'}=\left(3,-2\right)$
$A\text{'}=\left(-2,-1\right),B\text{'}=\left(-1,-5\right),C\text{'}=\left(-3,-2\right)$
$A\text{'}=\left(2,-1\right),B\text{'}=\left(1,-5\right),C\text{'}=\left(-3,2\right)$
$A\text{'}=\left(2,1\right),B\text{'}=\left(-1,5\right),C\text{'}=\left(-3,2\right)$
Question 7:   Find the triangle $ABC$ under a reflection in the $y$-axis, where $A=\left(2,-2\right),B=\left(1,2\right),C=\left(5,1\right)$
$A\text{'}=\left(-2,2\right),B\text{'}=\left(1,2\right),C\text{'}=\left(-5,1\right)$
$A\text{'}=\left(-2,2\right),B\text{'}=\left(-1,-2\right),C\text{'}=\left(-5,-1\right)$
$A\text{'}=\left(2,2\right),B\text{'}=\left(1,-2\right),C\text{'}=\left(5,-1\right)$
$A\text{'}=\left(-2,-2\right),B\text{'}=\left(-1,2\right),C\text{'}=\left(-5,1\right)$
Question 8:   Find the triangle $ABC$ under a reflection in the $y$-axis, where $A\left(-2,-2\right),B\left(-1,3\right),C\left(3,1\right)$
$A\text{'}=\left(2,-2\right),B\text{'}=\left(1,3\right),C\text{'}=\left(-3,1\right)$
$A\text{'}=\left(-2,2\right),B\text{'}\left(1,-3\right),C\text{'}=\left(3,1\right)$
$A\text{'}=\left(2,-2\right),B\text{'}\left(-1,-3\right),C\text{'}=\left(-3,-1\right)$
$A\text{'}=\left(-2,2\right),B\text{'}\left(-1,3\right),C\text{'}=\left(3,-1\right)$
Question 9:   Find the triangle $ABC$ under a reflection across the line $y=x$, where $A\left(2,3\right),B\left(7,4\right),C\left(6,-1\right)$
$A\text{'}=\left(-3,2\right),B\text{'}\left(-7,4\right),C\text{'}=\left(-1,-6\right)$
$A\text{'}=\left(-2,-3\right),B\text{'}=\left(7,-4\right),C\text{'}=\left(6,-1\right)$
$A\text{'}=\left(2,3\right),B\text{'}\left(4,7\right),C\text{'}=\left(-1,6\right)$
$A\text{'}=\left(2,-3\right),B\text{'}=\left(4,-7\right),C\text{'}=\left(6,-1\right)$
Question 10:   Find the triangle $ABC$ under a reflection across the line $y=x$, where $A\left(-3,1\right),B\left(3,-2\right),C\left(-2,4\right)$
$A\text{'}=\left(-1,-3\right),B\text{'}=\left(-2,3\right),C\text{'}=\left(4,-2\right)$
$A\text{'}=\left(-3,1\right),B\text{'}=\left(-3,-2\right),C\text{'}=\left(2,4\right)$
$A\text{'}=\left(3,-1\right),B\text{'}=\left(3,2\right),C\text{'}=\left(2,-4\right)$
$A\text{'}=\left(-1,3\right),B\text{'}=\left(2,-3\right),C\text{'}=\left(-4,-2\right)$