Reflection of the point (2, 3) on the X-axis is:
Understanding Reflection on the X-axis
Reflecting a point on the X-axis is a fundamental concept in coordinate geometry. When a point is reflected across the X-axis, its position changes relative to the X-axis.
Imagine the X-axis as a mirror. The reflected point is the same distance from the X-axis as the original point, but on the opposite side.
Rule for Reflection on the X-axis
The general rule for finding the reflection of a point \((x, y)\) on the X-axis is to change the sign of the y-coordinate while keeping the x-coordinate the same.
The reflection of the point \((x, y)\) on the X-axis is the point \((x, -y)\).
Applying the Rule to the Point (2, 3)
We are given the point (2, 3).
- The x-coordinate of the point is 2.
- The y-coordinate of the point is 3.
According to the rule for reflection on the X-axis, we keep the x-coordinate (2) the same and change the sign of the y-coordinate (from 3 to -3).
So, the reflected point is \((2, -3)\).
Comparing with the Options
Let's look at the given options:
- (-2, 3): This would be the reflection of (2, 3) on the Y-axis (changing the sign of the x-coordinate).
- (2, -3): This matches our calculated reflection on the X-axis.
- (-2, -3): This would be the reflection of (2, 3) on the origin (changing the sign of both coordinates).
- (3, 2): This involves swapping the coordinates, which is not a standard reflection on an axis or the origin.
Therefore, the reflection of the point (2, 3) on the X-axis is (2, -3).
| Reflection Across | Original Point \((x, y)\) | Reflected Point |
|---|---|---|
| X-axis | \((x, y)\) | \((x, -y)\) |
| Y-axis | \((x, y)\) | \((-x, y)\) |
| Origin | \((x, y)\) | \((-x, -y)\) |
| Line \(y = x\) | \((x, y)\) | \((y, x)\) |
Revision Table: Point Reflection Concepts
Reviewing the different types of reflections in coordinate geometry is helpful for exam preparation.
- Reflection across the X-axis: The y-coordinate changes sign.
- Reflection across the Y-axis: The x-coordinate changes sign.
- Reflection across the Origin: Both x and y coordinates change sign.
- Reflection across the line \(y = x\): The x and y coordinates swap positions.
Additional Information: Coordinate Geometry Basics
The coordinate plane is formed by two perpendicular number lines, the X-axis (horizontal) and the Y-axis (vertical), intersecting at the origin (0, 0). A point is located in this plane using an ordered pair \((x, y)\), where 'x' is the distance from the Y-axis (along the X-axis) and 'y' is the distance from the X-axis (along the Y-axis).
Understanding reflections helps in transforming geometric shapes and solving various problems in geometry and transformations.
Similar Questions
Find the slope of the line joining the points (3, -4) and (5, 2).
The graph of 2x = 5 - 3y cuts the x-axis at the point P (α, β) . The value of (2α + β) is:
Find the slope of the line given by the equation 4x + 6y = 9.
Find the slope of the line joining the points (3, -4) and (5, 2).
What is the distance between the points (4, 3) and (3, -2)?
Reflection of point (-2, -6) on the Y-axis is:
Find the coordinates of the midpoint of the segment joining the points (-4, 7) and (2, 3).
Important Questions from Co-ordinate Geometry
In which ratio the point (-3, p) divides the line segment joining the points (-5, -4) and (-2, 3)?
In which quadrant both abscissa and ordinate are negative?
Find the slope of the line joining the points (3, -4) and (5, 2).
A1 (x1, y1), A2 (x2, y2), A3 (x3, y3) and A4 (x4, y4) are 4 points, p1 divides A1A2 in the ratio 1 ∶ 1, p2 divides P1A3 in the ratio 1 ∶ 2, P3 divides p2A4 in the ratio 1 ∶ 3. Then the coordinates of p3 are:
If (3, 2) are coordinates of the centroid of a triangle, whose vertices are (0, 4), (-2, 0) and (p, 2), then find the value of p.
