Question

Rectangle ABCD went through a transformation and is now rectangle A'B'C'D'. Explain two different ways how rectangle ABCD becomes rectangle A'B'C'D'.

Answer 1

Answer:

when polar form the centre of the flower is transferred to the stigma of the same flower or stigma of another flower on the same plant this process is called self pollination

Answer 2

Given: See attachment for rectangles ABCD and $A'B'C'D$.

To determine: two possible ways of transformation.

Solution:

Observe the given question, ABCD coordinates:

$\[\begin{array}{l}A = \left( { - 6,5} \right)\\B = \left( { - 1,5} \right)\\C = \left( { - 1,1} \right)\\D = \left( { - 6,1} \right)\end{array}\]$

And $A'B'C'D'$ coordinates:

$\[\begin{array}{l}A' = \left( {5, - 1} \right)\\B' = \left( {5, - 6} \right)\\C' = \left( {1, - 6} \right)\\D' = \left( {1, - 1} \right)\end{array}\]$

Understand that, The first transformation is a rotation of ABCD by 90 degrees using the rule: $\[\left( {x,y} \right) \Rightarrow \left( {y, - x} \right)\]$.

Therefore,

$\[\begin{array}{l}A = \left( { - 6,5} \right) \Rightarrow \left( {5,6} \right)\\B = \left( { - 1,5} \right) \Rightarrow \left( {5,1} \right)\\C = \left( { - 1,1} \right) \Rightarrow \left( {1,1} \right)\\D = \left( { - 6,1} \right) \Rightarrow \left( {1,6} \right)\end{array}\]$

Translate 7 units down using the rule$\[\left( {x,y} \right) \Rightarrow \left( {x,y - 7} \right)\]$.

Thus,

$\[\begin{array}{l}\left( {5,6} \right) \Rightarrow \left( {5,6 - 7} \right)\\\left( {5,1} \right) \Rightarrow \left( {5,1 - 7} \right)\\\left( {1,1} \right) \Rightarrow \left( {1,1 - 7} \right)\\\left( {1,6} \right) \Rightarrow \left( {1,6 - 7} \right)\end{array}\]$

Therefore,

$\[\begin{array}{l}A' = \left( {5, - 1} \right)\\B' = \left( {5, - 6} \right)\\C' = \left( {1, - 6} \right)\\D' = \left( {1, - 1} \right)\end{array}\]$

Hence, a 90 degrees clockwise rotation about the origin and a translation of 7 units down is done.