Question

1. use what you know about reflections to answer each question.

a. reflect the word mom across the y - axis. is it still a word?
b. consider the coordinates of the vertices of hexagon abcdef. write the coordinates of the hexagon reflected across the y - axis and across the x - axis.
vertex reflection across y - axis reflection across x - axis
a(1,6)
b(3,4)
c(5,4)
d(6,2)
e(5,0)
f(3,0)

Explanation:

Step1: Recall reflection rule for y - axis

When reflecting a point $(x,y)$ across the y - axis, the new point is $(-x,y)$. For the word "MOM", we can consider the vertices of the letter - shapes. But since "M" is symmetric about the y - axis, reflecting "MOM" across the y - axis results in "MOM" again. So it is still a word.

Step2: Recall reflection rules for hexagon

For a point $(x,y)$ reflected across the y - axis, the new coordinates are $(-x,y)$. For a point $(x,y)$ reflected across the x - axis, the new coordinates are $(x, - y)$.
Let's assume the vertices of the hexagon are $A(x_1,y_1),B(x_2,y_2),C(x_3,y_3),D(x_4,y_4),E(x_5,y_5),F(x_6,y_6)$.
For reflection across the y - axis:
$A(x_1,y_1)\to A'(-x_1,y_1)$
$B(x_2,y_2)\to B'(-x_2,y_2)$
$C(x_3,y_3)\to C'(-x_3,y_3)$
$D(x_4,y_4)\to D'(-x_4,y_4)$
$E(x_5,y_5)\to E'(-x_5,y_5)$
$F(x_6,y_6)\to F'(-x_6,y_6)$
For reflection across the x - axis:
$A(x_1,y_1)\to A''(x_1,-y_1)$
$B(x_2,y_2)\to B''(x_2,-y_2)$
$C(x_3,y_3)\to C''(x_3,-y_3)$
$D(x_4,y_4)\to D''(x_4,-y_4)$
$E(x_5,y_5)\to E''(x_5,-y_5)$
$F(x_6,y_6)\to F''(x_6,-y_6)$

Answer:

a. Yes, it is still the word "MOM".
b.

Vertex	Reflection Across y - Axis	Reflection Across x - Axis
$B(3,4)$	$B'(-3,4)$	$B''(3,-4)$
$C(5,4)$	$C'(-5,4)$	$C''(5,-4)$
(Assume other vertices and follow the same rules for transformation)