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## Reflection in Lines Parallel to Axes Examples

**Example 1.**

The reflection of the point (4, -1) about the line 5x + y + 6 = 0 is

Solution:

**Given that**

The reflection point be A (h, k)

Now, the mid point of the line joining (h, k) and (4, -1) will lie on the line

5x + y + 6 = 0

Therefore

5(h+4)/2 + (k−1)/2 + 6 = 0

5h + 20 + k – 1 + 12 = 0

5h + k + 31 = 0……(i)

Now, the slope of the line joining points (h, k) and (4, -1) are perpendicular to the line is

5x + y + 6 = 0

Slope of the line=−5

Slope of the joining by points (h, k) and (4, -1)

k+1/h−4

Therefore

k+1/h−4(−5) = -1

5k − h + 69 = 0…..(ii)

Solving (i) and (ii), we get

5h + k + 6 – 5k + h – 69 = 0

6h – 4k – 63

h = 6 and k = -4

**Example 2.**

The point (-3, 0) on reflection in a line is mapped to (3, 0) and the point (4, -6) on reflection in the same line is mapped to (-4, -6).

(i) State the name of the mirror line and write its equation.

(ii) State the coordinates of the image of (-7, -5) in the mirror line.

**Solution:**

(i) We know the reflection of a point (x, y) in the y-axis is (-x, y).

Hence, the point (-3, 0) when reflected in the y-axis is mapped to (3, 0).

Therefore, the mirror line is the y-axis and its equation is x = 0.

(ii) Coordinates of the image of (-7, -5) in the mirror line in the y-axis are (7, -5).

**Example 3.**

The point (-4, 0) on reflection in a line is mapped as (4, 0) and the point (-7, -6) on reflection in the same line is mapped as (2, -6).

(a) Name the line of reflection.

(b) Write the coordinates of the image of (5, -9).

**Solution:**

(a) We know that reflection in line x = 0 is the reflection in the y-axis.

Given that the point is

Point (-4, 0) on reflection in a line is mapped as (4, 0).

Point (-7, -6) on reflection in the same line is mapped as (7, -6).

Hence, the line of reflection is x = 0.

(b) we know that

My (x, y) = (-x, y)

Coordinates of the image of (5, -9) in the line x = 0 are (-5, -9).

**Example 4.**

Point P(4, -3) is reflected as P’ in the y-axis. Point B on reflection in the x-axis is mapped as Q’ (-2, 7). Write the coordinates of P’ and Q.

**Solution:**

Given that the points are P(4,-3) and Q(-2,7)

Reflection in y-axis is given by

My (x, y) = (-x, y)

P’ = Reflection of P(4, -3) in y-axis

P’= (-4, -3)

Reflection in x-axis is given by

Mx (x, y) = (x, -y)

Q’ = Reflection of Q in x-axis = (-2, 7)

Therefore Q = (-2, -7)

**Example 5.**

The point (-3, 0) on reflection in a line is mapped as (3, 0) and the point (-8, -6) on reflection in the same line is mapped as (4, -6).

(a) Name the line of reflection.

(b) Write the coordinates of the image of (5, -6).

**Solution:**

(a) We know that reflection in line x = 0 is the reflection in the y-axis.

Given that the point is

Point (-3, 0) on reflection in a line is mapped as (3, 0).

Point (-8, -6) on reflection in the same line is mapped as (8, -6).

Hence, the line of reflection is x = 0.

(b) we know that

My (x, y) = (-x, y)

Coordinates of the image of (5, -6) in the line x = 0 are (-5, -6).

### FAQs on Reflection in Lines Parallel to Axes

**1. What does parallel to the axes mean?**

If a line is parallel to the x-axis or y-axis either the x-coordinate or y-coordinate is constant or fixed throughout the line and it should pass through either (0, a) or (a, 0).

**2. How do you reflect over the axis?**

A reflection of a point over the y -axis is. The rule for a reflection over the y -axis is (x,y) = (-x,y). And the reflection over the x- axis is (x,y) = (x,-y).

**3. What Does Parallel to the Axes Mean?**

Parallel to axes means that the lines are parallel to either the x-axis or y-axis.

If a line parallel to the x-axis is called a horizontal line whose equation is in the form of y = k,

where ‘k’ is the distance of the line from the x-axis.

Similarly, a line parallel to the y-axis is called a vertical line whose equation is in the form of x = k,

where ‘k’ is the distance of the line from the y-axis.