Question

reflect the quadrilateral abcd across the x - axis. plot the new points and draw the new triangle. record the new points below.
a(_, _) a(_, _)
b(_, _) b(_, _)
c(_, _) c(_, _)
d(_, _) d(_, _)

reflect the quadrilateral abcd across the y - axis. plot the new points and draw the new triangle. record the new points below.
a(_, _) a(_, _)
b(_, _) b(_, _)
c(_, _) c(_, _)
d(_, _) d(_, _)

reflect the quadrilateral abcd across the x and y - axis. plot the new points and draw the new triangle. record the new points below.
a(_, _) a(_, _)
b(_, _) b(_, _)
c(_, _) c(_, _)
d(_, _) d(_, _)

Explanation:

Step1: Recall reflection rules

When reflecting a point $(x,y)$ across the $x -$axis, the new point is $(x, - y)$. When reflecting a point $(x,y)$ across the $y -$axis, the new point is $(-x,y)$. When reflecting across both axes, the new point is $(-x,-y)$.

Step2: Reflect across x - axis

For a point $A(x,y)$, its reflection $A'$ across the $x -$axis has coordinates $(x,-y)$. For example, if $A(2,5)$, then $A'(2, - 5)$.

Step3: Reflect across y - axis

For a point $B(x,y)$, its reflection $B'$ across the $y -$axis has coordinates $(-x,y)$. For example, if $B(7,8)$, then $B'(-7,8)$.

Step4: Reflect across both x and y axes

For a point $C(x,y)$, its reflection $C'$ across both axes has coordinates $(-x,-y)$. For example, if $C(7,2)$, then $C'(-7,-2)$.

Answer:

For reflection across the $x$-axis:
If $A(2,5)$, then $A'(2,-5)$; if $B(7,8)$, then $B'(7,-8)$; if $C(7,2)$, then $C'(7,-2)$; if $D(2,2)$, then $D'(2,-2)$
For reflection across the $y$-axis:
If $A(2,5)$, then $A'(-2,5)$; if $B(7,8)$, then $B'(-7,8)$; if $C(7,2)$, then $C'(-7,2)$; if $D(2,2)$, then $D'(-2,2)$
For reflection across both $x$ and $y$ axes:
If $A(2,5)$, then $A'(-2,-5)$; if $B(7,8)$, then $B'(-7,-8)$; if $C(7,2)$, then $C'(-7,-2)$; if $D(2,2)$, then $D'(-2,-2)$