Question

reflections practice
name:
fill in the table and graph the image for each.

1. reflection across the x - axis

preimage (x, y)
m(-1, 2)
d(1, 3)
a(4, -5)
w(-1, -4)

image (, )
m(-1, -2)
d(1, -3)
a(4, 5)
w(-1, 4)

1. reflection across y = -x

preimage (x, y)
s(, )
t(, )
j(-1, )
a(, )

image (, )
s(, )
t(, )
j(, )
a(, )

Explanation:

Step1: Recall x-axis reflection rule

For a point $(x,y)$, reflection across the x-axis gives $(x,-y)$.

Step2: Calculate each image point

• $M(-4,5) \to M'(-4, -5)$
• $D(1,5) \to D'(1, -5)$
• $A(4,3) \to A'(4, -3)$
• $W(-4,4) \to W'(-4, -4)$

Step3: Recall $y=-x$ reflection rule

For a point $(x,y)$, reflection across $y=-x$ gives $(-y,-x)$.

Step4: Identify preimage points from graph

• $S(4,2)$, $T(2,1)$, $J(1,2)$, $A(3,3)$

Step5: Calculate each image point

• $S(4,2) \to S'(-2, -4)$
• $T(2,1) \to T'(-1, -2)$
• $J(1,2) \to J'(-2, -1)$
• $A(3,3) \to A'(-3, -3)$

Answer:

1) Reflection across the x-axis table:

Preimage (x,y)	Image (x,y)
$D(1,5)$	$D'(1,-5)$
$A(4,3)$	$A'(4,-3)$
$W(-4,4)$	$W'(-4,-4)$

(Graph note: Plot each image point and connect them to mirror the original shape below the x-axis)

2) Reflection across $y=-x$ table:

Preimage (x,y)	Image (x,y)
$T(2,1)$	$T'(-1,-2)$
$J(1,2)$	$J'(-2,-1)$
$A(3,3)$	$A'(-3,-3)$

(Graph note: Plot each image point and connect them to mirror the original shape across the line $y=-x$)