Question

fluency and skills practice
lesson 2
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(-3,6)
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 rules

Reflection across the y - axis changes the sign of the x - coordinate, while the y - coordinate remains the same. Reflection across the x - axis changes the sign of the y - coordinate, while the x - coordinate remains the same.

Step2: Solve for reflections across y - axis (for ABCDE)

For a point (x,y) reflected across the y - axis, the new point is (-x,y).
For example, if we assume the original x - coordinate of A was 3, after reflection across the y - axis, for A' the x - coordinate is - 3.
For B', if the original x - coordinate of B was some value x, the new x - coordinate is -x. Without knowing the original x - coordinate of B, we just follow the rule. If the original point B was (x,5), then B' is (-x,5).
For C', since it is a reflection across the y - axis and we know the new x - coordinate is - 4, if the original x - coordinate was 4, and since reflection across y - axis changes x to -x and y remains the same. But we don't know the original y - coordinate of C.
For D', since it is a reflection across the y - axis and we know the new x - coordinate is - 2, and we don't know the original y - coordinate of D.
For E', if the original x - coordinate of E was some value x, the new x - coordinate is -x. If the original point E was (x,4), then E' is (-x,4).

Step3: Solve for reflections across x - axis (for FGHIJ)

For a point (x,y) reflected across the x - axis, the new point is (x, - y).
For F', if the original y - coordinate of F was - 2, after reflection across the x - axis, the new y - coordinate is 2. But we don't know the original x - coordinate of F.
For G', if the original y - coordinate of G was - 2, after reflection across the x - axis, the new y - coordinate is 2. But we don't know the original x - coordinate of G.
For H', since it is a reflection across the x - axis and we know the x - coordinate is - 1, if the original y - coordinate was some value y, the new y - coordinate is -y.
For I', since it is a reflection across the x - axis and we know the x - coordinate is - 3, if the original y - coordinate was some value y, the new y - coordinate is -y.
For J', since it is a reflection across the x - axis and we know the x - coordinate is - 5, if the original y - coordinate was some value y, the new y - coordinate is -y.

Answer:

1. - 3 (assuming original x - coordinate of A was 3)
2. (No original x - coordinate of B given, just follow rule: -x if original was (x,5))
3. (No original y - coordinate of C given)
4. (No original y - coordinate of D given)
5. (No original x - coordinate of E given, just follow rule: -x if original was (x,4))
6. (No original x - coordinate of F given)
7. (No original x - coordinate of G given)
8. (No original y - coordinate of H given)
9. (No original y - coordinate of I given)
10. (No original y - coordinate of J given)