Question

May someone help me please and thank you

Answer 1

ANSWER :

A 180 degrees rotation about the origin.


EXPLANATION.

Let us name the vertices of the triangle as follows.

$A(1,1),B(4,1),C(3,2)$


If we reflect the triangle across the y-axis, then we have to negate the x-coordinates
to get,


$A'(-1,1),B'(-4,1),C'(-3,2)$




If we now reflect triangle ∆A'B'C' in the x-axis, we will have to negate the y-values to obtain,


$A''(-1,-1),B''(-4,-1),C''(-3,-2)$


The single transformation that will map ∆ABC to ∆A''B''C'' is
$(x,y)\rightarrow (-x,-y)$


This is a rotation of 180 degrees about the origin.