Question

performing a reflection in the coordinate plane

find the unknown coordinate for each reflection.

figure abcde is reflected across the y - axis to form figure abcde.
1 a( , 6)
2 b( , 5)
3 c(-4, )
4 d(-2, )
5 e( , 4)
figure fghij is reflected across the x - axis to form figure fghij.
6 f( , 2)
7 g( , 2)
8 h(-1, )
9 i(-3, )
10 j(-5, )

Explanation:

Step1: Recall reflection rule across y - axis

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

Step2: Find coordinates for ABCDE reflected across y - axis

1. For point A, assume original A is $(2,6)$ (from graph), after reflection across y - axis, $A'(- 2,6)$.
2. For point B, assume original B is $(4,5)$ (from graph), after reflection across y - axis, $B'(-4,5)$.
3. For point C, assume original C is $(4,2)$ (from graph), after reflection across y - axis, $C'(-4,2)$.
4. For point D, assume original D is $(2,2)$ (from graph), after reflection across y - axis, $D'(-2,2)$.
5. For point E, assume original E is $(1,4)$ (from graph), after reflection across y - axis, $E'(-1,4)$.

Step3: Recall reflection rule across x - axis

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

Step4: Find coordinates for FGHIJ reflected across x - axis

1. For point F, assume original F is $(-5,-2)$ (from graph), after reflection across x - axis, $F'(-5,2)$.
2. For point G, assume original G is $(-3,-2)$ (from graph), after reflection across x - axis, $G'(-3,2)$.
3. For point H, assume original H is $(-1,-4)$ (from graph), after reflection across x - axis, $H'(-1,4)$.
4. For point I, assume original I is $(-3,-6)$ (from graph), after reflection across x - axis, $I'(-3,6)$.
5. For point J, assume original J is $(-5,-4)$ (from graph), after reflection across x - axis, $J'(-5,4)$.

Answer:

1. -2
2. -4
3. 2
4. 2
5. -1
6. -5
7. -3
8. 4
9. 6
10. 4