In geometry, reflection is the type of transformation in the coordinate plane. A reflection is a mirror image of the given shape. In the previous articles, we have seen the reflection of a point in a plane, line, x-axis, y-axis, and origin. Let us discuss here the reflection of a point about a line formula from this page. Go through the examples given below and try to solve the problems in an easy manner.

**Also, Refer:**

- Reflection of a Point in the y-axis
- Reflection of a Point in the Origin
- Reflection of a Point in the x-axis

## Reflection of a Point in a Line – Definition

Reflection of a point is an interesting topic in the coordinate system. The reflection of the point in the x-axis means the x-coordinate remains the same and the y-coordinate sign will be changed. The reflection of the point in the y-axis means the y-coordinate remains the same and the x-coordinates sign will be changed.

### Reflection of a Point in a Line Examples

**Example 1.**

What is the reflection of the point (-1,3) on the line x = -3?

**Solution:**

The line x = -3 is a straight line parallel to the y-axis and at a distance of 3 units in the negative direction of the x-axis

Point (-1,3) is 3 units away from the given line x = -3.

Therefore the distance of the image from the line is also 3 units.

Thus the distance of image from y axis = 3+4+1 = 7.

Units in the negative direction of the x-axis.

Thus, the reflection of point (-1,3) in the line x = -3 is (-6,3).

**Example 2.**

What is the reflection of the point (1,2) in the line y = 4

**Solution:**

The line y = 4 bisects the line joining A and A’ the midpoint of these two points must lie on the line y = 4.

If we take point A’ as (a,b) the midpoint of A and A’ are

(1+1)/2, (b+3)/2 must satisfy the equation y = 4.

= (b+2)/2 = 4.

= b + 2 = 8

b = 6.

The required point is (1,6).

**Example 3.**

What is the reflection of the point (5,3) if the line is y = -6?

**Solution:**

The perpendicular distance between line y = -6.

And the point A(5,3) must be the same as the distance between line y = -6 and required reflection point P’

y = -6 is a line parallel to the x-axis.

Since the reflection is on the x-axis the x coordinate of P’ remains the same as 5.

y coordinate must be |-6| + 3 = 9 units away from the line y = -6.

The required y coordinate is -15.

Required point A’ = (5,-15).

**Example 4.**

What is the reflection of the point (-1,2) on the line x = -2.

**Solution:**

The line x = -2 is a straight line parallel to the y-axis and at a distance of 2 units in the negative direction of x-axis

Point (-1,2) is 2 units away from the given line x = -2.

Therefore the distance of the image from the line is also 2 units.

Thus the distance of image from y axis = 2+2+1 = 5.

Units in the negative direction of the x-axis.

Thus, the reflection of point (-1,2) in the line x = -2 is (-4,3).

**Example 5.**

What is the reflection of the point (1,3) in the line y = 5

**Solution:**

The line y = 5 bisects the line joining P and P’ the midpoint of these two points must lie on the line y = 5.

If we take point P’ as (a,b) the midpoint of P and P’ are

(1+1)/2, (b+3)/2 must satisfy the equation y = 4.

= (b+2)/2 = 5.

= b + 2 = 10

b = 8

Required point is (1,8).

### FAQs on Reflection of a Point in a Line

**1. What is a reflection line?**

A reflection is a transformation, it means flipping of a figure. Figures may be reflected in a point, line, or a plane. When reflecting a figure in a line or in a point, then the image is congruent to the preimage. The fixed line is called the line of reflection.

**2. How do you write a line of reflection?**

The line of reflection is given in the form of y = mx + b. And draw the line of reflection using the point in the starting figure that is the same perpendicular distance from the line of reflection as its corresponding point in the image.

**3. What does reflection across y = 2 mean?**

The x-value of the mirror image will be the same. At the y-values. the y-values must be the same number of units below the line y = 2 as above the line y = 2.