Mirror and Water Imagesदर्पण और जल प्रतिबिंब questions and answersप्रश्न और उत्तर

How mirror and water images worksदर्पण और जल प्रतिबिंब को समझिए

A mirror held upright on the right (or left) of a figure swaps left and right. A point near the mirror stays near the mirror; a point far from it stays far, now on the other side. Nothing moves up or down, so the top of the figure is still the top.

A water image is the reflection in a horizontal line, such as the surface of a lake below the figure. Now top and bottom swap and left–right positions stay. An arrow pointing up becomes an arrow pointing down at the same left–right position.

Examiners always include the figure turned through 180° as an option, because it looks reflected. A half turn swaps both left–right and top–bottom; it is what you get by taking the mirror image and then the water image. A single reflection never does both.

Each trick says when to use it, why it works and when it fails. Formula tricks are checked by code over their whole range.हर ट्रिक बताती है कि उसे कब इस्तेमाल करें, वह क्यों काम करती है और कब नहीं। सूत्र वाली ट्रिक्स को कोड से उनकी पूरी रेंज पर जाँचा गया है।

Answers and full solutions are shown. Hide them to test yourself first.उत्तर और पूरे हल दिखाए गए हैं। पहले खुद को परखने के लिए इन्हें छिपाइए।

1. Example 1उदाहरण 1 · Mirror images of figures · Easyआसान

   A mirror is held along the dashed line to the right of the question figure. Which answer figure is its mirror image?

   1. A
   2. B
   3. C
   4. D
   Answer:उत्तर: D

   1. In a mirror image every point keeps its height and moves to the same distance on the other side: (x, y) → (3 − x, y).
   2. The arrowhead at (1, 0) goes to (2, 0), and every stroke moves the same way.
   3. Only figure (D) has every part in its reflected place, so the answer is (D).

2. Example 2उदाहरण 2 · Water images of figures · Easyआसान

   The dashed line below the question figure is the surface of still water. Which answer figure is its water image (reflection in the water)?

   1. A
   2. B
   3. C
   4. D
   Answer:उत्तर: C

   1. In a water image every point keeps its left–right position and moves to the same distance on the other side vertically: (x, y) → (x, 3 − y).
   2. The arrowhead at (1, 1) goes to (1, 2), and every stroke moves the same way.
   3. Only figure (C) has every part in its reflected place, so the answer is (C).

3. Example 3उदाहरण 3 · Mirror images of figures · Mediumमध्यम

   A mirror is held along the dashed line to the right of the question figure. Which answer figure is its mirror image?

   1. A
   2. B
   3. C
   4. D
   Answer:उत्तर: C

   1. In a mirror image every point keeps its height and moves to the same distance on the other side: (x, y) → (4 − x, y).
   2. The arrowhead at (3, 0) goes to (1, 0), and every stroke, dot moves the same way.
   3. Only figure (C) has every part in its reflected place, so the answer is (C).

4. Example 4उदाहरण 4 · Water images of figures · Mediumमध्यम

   The dashed line below the question figure is the surface of still water. Which answer figure is its water image (reflection in the water)?

   1. A
   2. B
   3. C
   4. D
   Answer:उत्तर: A

   1. In a water image every point keeps its left–right position and moves to the same distance on the other side vertically: (x, y) → (x, 4 − y).
   2. The arrowhead at (2, 3) goes to (2, 1), and every stroke, dot moves the same way.
   3. Only figure (A) has every part in its reflected place, so the answer is (A).

5. Example 5उदाहरण 5 · Mirror images of figures · Hardकठिन

   A mirror is held along the dashed line to the right of the question figure. Which answer figure is its mirror image?

   1. A
   2. B
   3. C
   4. D
   Answer:उत्तर: B

   1. In a mirror image every point keeps its height and moves to the same distance on the other side: (x, y) → (4 − x, y).
   2. The arrowhead at (2, 3) goes to (2, 3), and every stroke, dot and circle moves the same way.
   3. Only figure (B) has every part in its reflected place, so the answer is (B).

6. Example 6उदाहरण 6 · Water images of figures · Hardकठिन

   The dashed line below the question figure is the surface of still water. Which answer figure is its water image (reflection in the water)?

   1. A
   2. B
   3. C
   4. D
   Answer:उत्तर: B

   1. In a water image every point keeps its left–right position and moves to the same distance on the other side vertically: (x, y) → (x, 4 − y).
   2. The arrowhead at (4, 2) goes to (4, 2), and every stroke, dot and circle moves the same way.
   3. Only figure (B) has every part in its reflected place, so the answer is (B).

Common mistakesआम गलतियाँ

• Choosing the 180° turn: it swaps both directions, while a reflection swaps only one.
• Confusing mirror and water images, especially when the options are drawn small. Ask first: is the line beside the figure or below it?
• Reflecting the main strokes but leaving a small dot or circle where it was. Every part of the figure is reflected.

Frequently asked questionsअक्सर पूछे जाने वाले प्रश्न