Class 10 Exam > Class 10 Notes > Mathematics Class 10 ICSE > Revision Notes: Coordinate Geometry - Reflection
Revision Notes: Coordinate Geometry - Reflection | Mathematics Class 10 ICSE PDF Download
Important Concepts
- The mutual perpendicular lines intersecting each other at their zeroes are called rectangular axes or coordinate axes
- Horizontal axis is called x-axis and the vertical axis is called y-axis.
- (0, 0) is the called the origin.
- The position of a point in a plane is expressed by a pair of two numbers called coordinates.
- Reflection is a map that transforms an object into its mirror image.
- A point which does not change upon undergoing a certain reflection is said to have reflection symmetry and is known as the invariant point.
- When the reflection takes place in the x-axis, retain the abscissa as it is, but change the sign of the ordinate.
- When the reflection takes place in the y-axis, retain the ordinate as it is, but change the sign of the abscissa.
- When reflection takes place in the origin, change the sign of both the coordinates.
- MX means reflection in the x-axis.
- My means reflection in the y-axis.
- Mo means reflection in the origin.
- MXMY means that the point is first reflected in the x-axis and then in the y-axis.
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FAQs on Revision Notes: Coordinate Geometry - Reflection - Mathematics Class 10 ICSE
| 1. What is reflection in coordinate geometry? |  |
Ans. Reflection in coordinate geometry refers to the flipping of a point or shape over a specific line, known as the line of reflection. The reflected point maintains the same distance from the line of reflection as the original point but lies on the opposite side. For example, reflecting a point across the x-axis involves changing the y-coordinate from \( (x, y) \) to \( (x, -y) \).
| 2. How do you find the coordinates of a point after reflection across the y-axis? | |
Ans. To find the coordinates of a point after reflection across the y-axis, you change the sign of the x-coordinate while keeping the y-coordinate the same. For example, if the original point is \( (a, b) \), the reflected point across the y-axis will be \( (-a, b) \).
| 3. What are the steps to reflect a triangle across a line in coordinate geometry? | |
Ans. To reflect a triangle across a line, follow these steps:
1. Identify the coordinates of the triangle's vertices.
2. Determine the equation of the line of reflection.
3. For each vertex, calculate the perpendicular distance to the line to find the foot of the perpendicular.
4. Use the foot of the perpendicular to find the reflected point by moving the same distance on the opposite side of the line.
5. Plot the new vertices to visualize the reflected triangle.
| 4. Can you provide an example of reflecting a point across the line y = x? | |
Ans. Yes! To reflect a point across the line \( y = x \), you simply swap the x and y coordinates. For instance, if the original point is \( (3, 5) \), the reflected point across the line \( y = x \) will be \( (5, 3) \).
| 5. How do you determine the line of reflection for two given points that are reflections of each other? | |
Ans. The line of reflection for two points that are reflections of each other is the perpendicular bisector of the line segment joining the two points. First, find the midpoint of the segment, which will give you a point on the line of reflection. Next, find the slope of the line segment and then determine the negative reciprocal to find the slope of the perpendicular bisector. Using the midpoint and the new slope, you can write the equation of the line of reflection.
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