Question

graph the given reflection. write the coordinates of the pre - image and image.

1. reflect over the x - axis

a(__, ) b(, __)
a(__, ) b(, __)

1. reflect over the y - axis

x(__, ) y(, __)
x(__, ) y(, __)

1. $\triangle abc$ over $y = x$

a(__, ) a(, __)
b(__, ) b(, __)
c(__, ) c(, __)

1. $\triangle xyz$ over $x = - 1$

x(__, ) x(, __)
y(__, ) y(, __)
z(__, ) z(, __)

Explanation:

Step1: Identify pre-image coordinates (Q9)

From graph: $A(-4, 8)$, $B(2, 6)$

Step2: Apply x-axis reflection (Q9)

Rule: $(x,y)\to(x,-y)$
$A'(-4, -8)$, $B'(2, -6)$

Step3: Identify pre-image coordinates (Q10)

From graph: $X(-2, 8)$, $Y(2, -4)$

Step4: Apply y-axis reflection (Q10)

Rule: $(x,y)\to(-x,y)$
$X'(2, 8)$, $Y'(-2, -4)$

Step5: Identify pre-image coordinates (Q11)

From graph: $A(-2, 5)$, $B(-1, 1)$, $C(-6, 2)$

Step6: Apply $y=x$ reflection (Q11)

Rule: $(x,y)\to(y,x)$
$A'(5, -2)$, $B'(1, -1)$, $C'(2, -6)$

Step7: Identify pre-image coordinates (Q12)

From graph: $X(1, 4)$, $Y(1, -2)$, $Z(5, -2)$

Step8: Apply $x=-1$ reflection (Q12)

Rule: $(x,y)\to(-2-x,y)$
$X'(-3, 4)$, $Y'(-3, -2)$, $Z'(-7, -2)$

Answer:

Question 9:

$A(-4, 8)$ $B(2, 6)$
$A'(-4, -8)$ $B'(2, -6)$

Question 10:

$X(-2, 8)$ $Y(2, -4)$
$X'(2, 8)$ $Y'(-2, -4)$

Question 11:

$A(-2, 5)$ $A'(5, -2)$
$B(-1, 1)$ $B'(1, -1)$
$C(-6, 2)$ $C'(2, -6)$

Question 12:

$X(1, 4)$ $X'(-3, 4)$
$Y(1, -2)$ $Y'(-3, -2)$
$Z(5, -2)$ $Z'(-7, -2)$