OP Malhotra Class 10 Maths Solutions Chapter 10 Reflection Exercise 10 (A)

Question 1. Copy the figure and show the images which result from reflection in the line m.
Answer: The figures below show the original shapes and their reflected images across the line of reflection 'm'. Each point in the original figure is moved to an equal distance on the opposite side of line 'm' to form its image. This creates a mirror image, maintaining the shape and size but flipping its orientation.
In simple words: Look at each picture, and imagine the line 'm' is a mirror. Draw the exact same shape on the other side of the mirror. It will look like a flipped version of the original.

🎯 Exam Tip: When drawing reflections, remember that the image is always the same distance from the mirror line as the original object, but on the opposite side. This is key for accuracy.

Question 2. Reflect the circle with arrow in the line m in the figure.
Answer: We draw a new circle with its center O' located at the mirror image of the original center O. This new circle is the reflection of the given circle across the line 'm'. The arrow will also be reflected, pointing in the opposite direction relative to the line of reflection.
In simple words: Imagine the line 'm' is a mirror. Draw the circle on the other side of the mirror so it looks exactly like the first one, but flipped.

🎯 Exam Tip: For reflecting circles, remember that only the center point needs to be reflected. The reflected circle will have the same radius as the original. Also ensure any internal features like arrows are correctly reflected.

Question 3. In the figure, mark accurately.
(i) P\( _1 \) is the image of P under reflection in line AB.
(ii) P\( _2 \) is the image of P under reflection in line BC.
(iii) P\( _3 \) is the image of P under reflection in line CA.
What do you observe about the points P\( _1 \), P\( _2 \) and P\( _3 \).

Answer: We mark P\( _1 \) as the reflection of P across line AB, P\( _2 \) as the reflection of P across line BC, and P\( _3 \) as the reflection of P across line CA. After marking these points, we observe that P\( _1 \), P\( _3 \), and P\( _2 \) all lie on the same straight line. This line is parallel to line CA, and it passes through point B. This geometric property shows how multiple reflections can create collinear points.
In simple words: We find the mirror image of point P across line AB (called P1), across line BC (called P2), and across line CA (called P3). When we look at P1, P2, and P3, they all fall on one straight line. This line is also parallel to the side CA of the triangle and goes through corner B.

🎯 Exam Tip: When reflecting a point across a line, remember to draw a perpendicular line from the point to the reflection line, and then extend it an equal distance on the other side. Use a ruler and protractor for accurate construction.

Question 4. Answer true or false : Under reflection, lines which are parallel to the mirror, have image, which is also parallel to the mirror line.
Answer: True. When you reflect a line that is parallel to the mirror line, its image will also be parallel to that same mirror line. The distance between the image line and the mirror line will be the same as the distance between the original line and the mirror line. Reflection preserves parallelism.
In simple words: If a line is perfectly straight and never touches the mirror line, its reflection will also be perfectly straight and never touch the mirror line, staying parallel to it.

🎯 Exam Tip: Remember that reflection is an isometric transformation, meaning it preserves distances, angles, and parallelism. This is a fundamental property to recall for such true/false questions.