Transformations

The coordinate point of $\left(-1,3\right)$ is reflection in the $X$-axis followed by a rotation about origin through $90°$ is

The coordinate point of $\left(1,3\right)$ is reflection in the $X$-axis followed by a rotation about origin through $90°$ is

_____ transformations is doing more than one transformation on a geometric shape.

Define combining transformations.

The original vertices of a triangle are $\left(3,2\right), \left(1,9\right)$ and $\left(-6,4\right)$. The vertices of the image of the triangle are $\left(9,-2\right), \left(7,-9\right)$ and $\left(12,-4\right)$. The two different sets of two transformations that could have occurred are,

For the following shapes, specify the translation that has occurred. 

For the following shapes, specify the translation that has occurred. 

On squared paper, copy the following shape and translate it to $5$ units down and $2$ units left. 

On squared paper, copy the following shape and translate it to $6$ units up and $3$ units right. 

On squared paper, copy the following shape and translate it to $1$ unit up and $7$ units left, $4$ units down, $9$ units right. Could the instructions for translation be simplified so that the translation can be completed in fewer steps? Explain.

On squared paper, copy each shape and translate it by the specified units. 

i) 

$5$ units down, $2$ units left

ii)

$6$ units up, $3$ units right

iii)

$1$ unit up and $7$ units left, $4$ units down, $9$ units right. 

Write the three translations using correct notation.

Given, vertices of a quadrilateral are $\left(1,8\right), \left(-3,-5\right), \left(-4,7\right)$ and $\left(-6,-2\right)$. Then plot the image of this shape after each of these translations.

a) $\left(x,y\right) \mapsto \left(x-3,y\right)$

b) $\left(x,y\right) \mapsto \left(x,y+5\right)$

c) $\left(x,y\right) \mapsto \left(x+6,y+1\right)$

d) $\left(x,y\right) \mapsto \left(x-2,y-4\right)$

Given the translation $\left(x,y\right) \mapsto \left(x-4,y+1\right)$, find the preimage of the image point $\left(-6,15\right)$.

Given the rotation $\left(x,y\right)\mapsto \left(-y,x\right)$, find the image of the preimage point $\left(5,9\right)$ and describe the rotation in words.

Given the rotation $\left(x,y\right)\mapsto \left(-y,x\right)$, find the image of the preimage point $\left(-2,0\right)$ and describe the rotation in words.

Given the rotation $\left(x,y\right)\mapsto \left(-y,x\right)$, find the image of the preimage point $\left(0,-8\right)$ and describe the rotation in words.

Given the rotation $\left(x,y\right)\mapsto \left(-x,-y\right)$, find the image of the preimage point $\left(-6,15\right)$ and describe the rotation in words.

Given the rotation $\left(x,y\right)\mapsto \left(-x,-y\right)$, find the image of the preimage point $\left(13,-11\right)$ and describe the rotation in words.

Given the rotation $\left(x,y\right)\mapsto \left(-x,-y\right)$, find the image of the preimage point $\left(0,0\right)$ and describe the rotation in words.

Copy and complete the table below: