Reflection is one of the easiest chapters at the secondary level. The worksheet on reflection in the origin with solutions is available on this page. In the concept of reflection in the origin, both the coordinates in the x-axis and y-axis signs are changed. In a point reflection in the origin, the image of the point (x,y) is the point (-x,-y). The students can find different types of problems related to the reflection in the origin from here.

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## Worksheet on Reflection in the Origin

**Example 1.**

Find the reflection of the point P(0,10) in the origin.

**Solution:**

Given that the point is P(0,10)

The reflection of the point H (0, 10) in the origin is the point H’ (0, -10)

**Example 2.**

The point (a,b) is first reflected in the origin and then reflected in the y-axis to P’. If P’ has coordinates (4,6). Evaluate a and b.

**Solution:**

Mo(a,b) = (-a, -b)

My(-a,-b) = (a,-b)

Thus, we get the coordinates of the given point P’ as (a,-b).

It is given that the coordinates of P’ are (4,6).

On comparing the two points we get a = 4, b = -6.

**Example 3.**

The point P(x, y) is first reflected in the x- axis and reflected in the origin to P’ if P’ has coordinates (-8,5), evaluate x and y.

**Solution:**

MX(x,y) = (x,-y)

Mo(x,y) = (-x,y)

Thus we get the coordinates of the point P’ as (-x,y)

If it is given that the coordinates of P’are (-8,5) on comparing the two points we get x = 8. and y = 5.

**Example 4.**

What is the reflection of the point A(4 5) in origin?

**Solution:**

Given that A(4,5)

The image of A (2, 5) is P’ (-4, -5).

**Example 5.**

The triangle ABC where A is (2,4) B is (2,6) and Cis (3,8) is reflected in the y- axis to triangle A’B’C’. Triangle A’B’C’ is then reflected in the origin to triangle A”B”C”.

(i) write down the coordinates of A”B”C”

(ii) write down the single transformation that maps triangle ABC onto triangle A”B”C”.

**Solution:**

(i) reflection in y axis is given by My(-x,y)

Therefore A’ = reflection of A(2,4) in y axis = (-2,4)

Similarly B’ = (2,6) and C’ = (-3,8)

Reflection in origin is given by Mo (x,y) = (-x,-y)

A” = Reflection of A'(-2,4) in origin (2,-4)

Similarly B’ = (-3,-5) and (3,-8)

(ii) A single transaction that maps triangle ABC to triangle A”B”C” is a reflection in the x axis.

**Example 6.**

P and Q have coordinates (-4,3) and (5,6) respectively. Respect P in the x axis to P’ and Q in the y axis to Q1. State the coordinates of P’ and Q’.

**Solution:**

Reflection in x axis is given by Mx(x,y) = (x,-y)

P’ = reflection of P(-4,3) in x axis = (-4,-3)

Reflection in y axis is given by My(x,y) = (-x,y)

Q’ = reflection od Q(5,6) in y axis = (-5,6)

Thus the coordinates of the point P’ and Q’ are (-2,-3) and (-5,4) respectively.

**Example 7.**

Point P(a,b) is reflected in the x axis to P'(3,-4) write down the values of a and b.

**Solution:**

We know that MX(x,y) = (x,-y)

P'(3,4) = reflection of P(a,b) in x axis.

Thus the coordinates of P’ are (3,4)

Hence a = 3, b = 4.

**Example 8.**

What is the reflection of the point A(2, 7) in origin?

**Solution:**

Given that A(2,7)

The image of A (2, 7) is P’ (-2, -7).

**Example 9.**

What is the reflection of the point A(8, 5) in origin?

**Solution:**

Given that A(8,5)

The image of A (8, 5) is P’ (-8, -5).

**Example 10.**

What is the reflection of the point A(3, 9) in origin?

**Solution:**

Given that A(3,9)

The image of A (3, 9) is P’ (-3, -9).