L62 — Reflections — Solutions

1. Reflect over the x-axis

   1. (2, −5) ▶ View Solution
   2. (4, 3) ▶ View Solution
   3. (−1, −7) ▶ View Solution
   4. (0, −6) ▶ View Solution

2. Reflect over the y-axis

   1. (−3, 4) ▶ View Solution
   2. (5, 2) ▶ View Solution
   3. (−7, −1) ▶ View Solution
   4. (0, 3) — point is on y-axis, unchanged ▶ View Solution

3. Reflect over y = x

   1. (7, 2) ▶ View Solution
   2. (1, 4) ▶ View Solution
   3. (5, −3) ▶ View Solution
   4. (6, 0) ▶ View Solution

4. Reflect Shapes

   1. A(1,2) B(4,2) C(2,5) over x-axis: A′(1,−2), B′(4,−2), C′(2,−5) ▶ View Solution
   2. P(−1,3) Q(2,3) R(0,6) over y-axis: P′(1,3), Q′(−2,3), R′(0,6) ▶ View Solution
   3. D(1,1) E(4,1) F(4,3) G(1,3) over x-axis: D′(1,−1), E′(4,−1), F′(4,−3), G′(1,−3) ▶ View Solution
   4. J(2,3) K(5,1) L(3,6) over y = x: J′(3,2), K′(1,5), L′(6,3) ▶ View Solution

5. Identify the Mirror Line

   1. x-axis ▶ View Solution
   2. y-axis ▶ View Solution
   3. y = x ▶ View Solution
   4. y-axis ▶ View Solution

6. Reflections in Context

   1. A = (2, 4); B = (5, 4); C = (3, 7) ▶ View Solution
   2. (−6, 3) ▶ View Solution
   3. Kaleidoscope — (1,0)(3,0)(2,2) over x-axis then y-axis: Over x-axis: (1,0)(3,0)(2,−2)  |  Over y-axis: (−1,0)(−3,0)(−2,2) ▶ View Solution
   4. P(a,b) over x-axis then y-axis: P′′ = (−a, −b) — same as a 180° rotation about the origin ▶ View Solution

7. Mixed Reflection Practice

   1. (i) (3,−1)   (ii) (−3,1)   (iii) (1,3) ▶ View Solution
   2. (i) (−4,−2)   (ii) (4,2)   (iii) (2,−4) ▶ View Solution
   3. (i) (5,5)   (ii) (−5,−5)   (iii) (−5,5) ▶ View Solution
   4. (i) (0,−4)   (ii) (0,4) — unchanged   (iii) (4,0) ▶ View Solution

8. Reflection on a Grid — Describe and Apply

   1. (4,3) → (−4,3): Mirror line: y-axis; rule: (x,y) → (−x,y) ▶ View Solution
   2. (2,5) → (2,−5): Mirror line: x-axis; rule: (x,y) → (x,−y) ▶ View Solution
   3. Triangle (1,2)(3,4)(5,1) over x-axis then y-axis: Over x-axis: (1,−2),(3,−4),(5,−1)  |  Over y-axis: (−1,−2),(−3,−4),(−5,−1)  |  Equivalent: 180° rotation about the origin ▶ View Solution
   4. Why reflection changes orientation but not size: All lengths are preserved (each point maps the same distance from the mirror line), but vertex order reverses (clockwise becomes anticlockwise) ▶ View Solution

9. Reflections — Find the Missing Coordinate

   1. −5 — mirror line: x-axis ▶ View Solution
   2. ? = 7 — mirror line: y-axis ▶ View Solution
   3. ? = 3 — mirror line: y = x ▶ View Solution
   4. ? = −3 — mirror line: y = x ▶ View Solution

10. Reflections in the Real World

    1. (0,0), (0,8), (−3,8), (−3,5), (−5,5), (−5,0) ▶ View Solution
    2. Triangle (0,0)(4,0)(0,3) over y-axis and x-axis: y-axis: (0,0),(−4,0),(0,3)  |  x-axis: (0,0),(4,0),(0,−3) ▶ View Solution
    3. (5, −6); distance between original and image = 12 units ▶ View Solution
    4. After reflection: (−3, 2); after walking right 5: (2, 2) ▶ View Solution