Question

geometry ii
9.2 reflections (worksheet)
graph the image of the figure using the transformation given.

1. reflection across the y - axis
2. reflection across the x - axis
3. reflection across the x - axis
4. reflection across the y - axis
5. reflection across the y - axis
6. reflection across the y - axis

Explanation:

Step1: Identify original coordinates (1)

Original points: $N(-4,1)$, $F(-2,0)$, $P(1,-2)$, $W(-4,-3)$

Step2: Reflect over y-axis (1)

Rule: $(x,y)\to(-x,y)$
New points: $N'(4,1)$, $F'(2,0)$, $P'(-1,-2)$, $W'(4,-3)$

Step3: Identify original coordinates (2)

Original points: $J(2,0)$, $I(4,0)$, $K(5,-1)$, $H(2,-3)$

Step4: Reflect over x-axis (2)

Rule: $(x,y)\to(x,-y)$
New points: $J'(2,0)$, $I'(4,0)$, $K'(5,1)$, $H'(2,3)$

Step5: Identify original coordinates (3)

Original points: $D(-3,-1)$, $E(-1,2)$, $F(0,2)$, $G(0,1)$

Step6: Reflect over x-axis (3)

Rule: $(x,y)\to(x,-y)$
New points: $D'(-3,1)$, $E'(-1,-2)$, $F'(0,-2)$, $G'(0,-1)$

Step7: Identify original coordinates (4)

Original points: $P(-1,0)$, $Q(2,3)$, $R(3,1)$

Step8: Reflect over y-axis (4)

Rule: $(x,y)\to(-x,y)$
New points: $P'(1,0)$, $Q'(-2,3)$, $R'(-3,1)$

Step9: Identify original coordinates (5)

Original points: $K(-6,-1)$, $J(-3,-1)$, $M(-4,-3)$

Step10: Reflect over y-axis (5)

Rule: $(x,y)\to(-x,y)$
New points: $K'(6,-1)$, $J'(3,-1)$, $M'(4,-3)$

Step11: Identify original coordinates (6)

Original points: $Q(2,3)$, $P(1,1)$, $S(1,-2)$, $V(3,-3)$

Step12: Reflect over y-axis (6)

Rule: $(x,y)\to(-x,y)$
New points: $Q'(-2,3)$, $P'(-1,1)$, $S'(-1,-2)$, $V'(-3,-3)$

Answer:

1. Reflected points: $N'(4,1)$, $F'(2,0)$, $P'(-1,-2)$, $W'(4,-3)$ (connect these to graph the image)
2. Reflected points: $J'(2,0)$, $I'(4,0)$, $K'(5,1)$, $H'(2,3)$ (connect these to graph the image)
3. Reflected points: $D'(-3,1)$, $E'(-1,-2)$, $F'(0,-2)$, $G'(0,-1)$ (connect these to graph the image)
4. Reflected points: $P'(1,0)$, $Q'(-2,3)$, $R'(-3,1)$ (connect these to graph the image)
5. Reflected points: $K'(6,-1)$, $J'(3,-1)$, $M'(4,-3)$ (connect these to graph the image)
6. Reflected points: $Q'(-2,3)$, $P'(-1,1)$, $S'(-1,-2)$, $V'(-3,-3)$ (connect these to graph the image)