#### Need Help?

Get in touch with us

The component learnSearchBar has not been created yet.

# Reflection of Image On a Coordinate Plane

### Key Concepts

• Understanding reflection
• Reflection of figure on a coordinate plane
• Describe reflection

## Reflection of Image

The coordinate plane and points on different quadrants of coordinate plane. In the first quadrant, both x and y are positive or (x, y) is positive. In second quadrant, x is negative, and y is positive or
(-x, y) lies in the second quadrant.

In the third quadrant, both x and y are negative or (-x, -y) lies in the third quadrant.

In fourth quadrant, x is positive, and y is negative or
(x, -y) lies in the fourth quadrant.

Coordinates of a point x-axis is (x, 0). Coordinates of a point y-axis is (0, y).

Coordinates of origin O is (0, 0).

x-coordinate is called abscissa.

y-coordinate is called ordinate.

### Reflection of an image on a coordinate plane

What is reflection?

When an object is placed before a plane mirror, the image is formed at the same distance behind the mirror as the object is in front of it.

That is, if P is the image, then P’ is the reflected image formed.

Transformation is where each point in a shape appears at an equal distance on the opposite side of a given line.

Reflection with respect to that line is called the line of reflection.

The image is flipped across a line.

Since there is no chance of change in size or shape of the image and this transformation is isometric.

### Understanding of reflection

Reflection line

Reflection in the line y= 0 or x-axis

When a point is reflected in the x- axis, the sign of ordinate changes or y coordinate changes.

If P is the image and P’ is the reflected image then the point P(x , y) changes to

P’(x ,-y).

Reflection in the line x = 0 or y-axis

When a point is reflected in the y- axis, the sign of abscissa changes or x coordinate changes.

If P is the image, and P’ is the reflected image then the point P(x , y) changes to

P’(-x , y).

Reflection in the origin

When a point P(x , y) is reflected in the origin, the sign of its abscissa and ordinate both

changes. If P (x, y ) is a point in the image, then point in the reflected image is P’(-x , -y) .

Reflection in the line when y =x and y= -x

Reflection of a point (x , y ) at y=x is ( y, x) and reflection of a point (x , y) at y= -x

is (-y , -x)

#### Reflect ΔABC Over the Y-Axis

Reflection at the Origin

Reflection at Y=X

Reflection at y= -x

### Reflection rules in the coordinate plane

Reflection across x-axis

Reflection across y=x

### Describe Reflection

Write a rule to describe the transformation.

Reflection across x-axis

1. Reflection across x axis (4, 2) is (4, -2)
1. Reflection across y axis (-2, 3) is (2, 3)
1. Reflection at origin (3, 0) is (-3, 0)
1. Find the reflection of the point P (-1, 3) in the line x=2.

If P’ is the point of reflection, then P’ (5, 3) is the reflection of P (-1, 3) in the line x=2.

1. Find the reflection of the point Q (2, 1) in the line y + 3 =0.

If Q’ is the point of reflection, then Q’ (2, -7) is the reflection of Q (2, 1) in the line

y+3 =0.

1. The points A (2, 3), B (4, 5), and C (7, 2) are the vertices of triangle ABC. Write down

the coordinates A’, B’, C’, if triangle A’B’C’ is the reflected image of triangle ABC

when reflected in the origin.

## Exercise:

1. Find the reflection of the following in y-axis.
2. (-2, -6)                                  ii.     (1, 7)                       iii.     (-3, 1)
3. The coordinates of the points under reflection in origin.
4. (-2, -4)                                  ii.     (-2, 7)                      iii.     (3, 1)
5. The point P is reflected in the origin. Coordinates of its image are (-2, 7). Find the coordinates of P.
6. The point P (x, y) is reflected in the x-axis and then reflected in the origin to P’. If P’ has coordinates (-8, 5). Evaluate x, y.
7. Point A (4, -1) is reflected as A’ in y-axis. Point B on reflection in the y-axis is B’ (-2, 5). Write the coordinates of A’ and B.
8. The point (-5, 0) on reflection in a line is (5, 0) and the point (-2, -6) on reflection in the same line is (2, -6). Write the line of reflection. Write the coordinates of the image of (5, -8) in the line of reflection.
9. The points P (1, 2), Q (3, 4) and R (6, 1) are vertices of a triangle PQR. Write down the coordinates of P’, Q’ and R’ if the triangle P’Q’R’ is the image reflected in the origin?
10. The point P is reflected in the x-axis. Coordinates of its image are (8, -6).
11. Find the coordinates of P.
12. Find the coordinates of the image of P under reflection in the y-axis.

### What we have learned:

• We learned another form of transformation reflection.
• Understand the transformation reflection in a coordinate plane.
• Describe the transformation reflection

### Concept Map:

#### Composite Figures – Area and Volume

A composite figure is made up of simple geometric shapes. It is a 2-dimensional figure of basic two-dimensional shapes such as squares, triangles, rectangles, circles, etc. There are various shapes whose areas are different from one another. Everything has an area they occupy, from the laptop to your book. To understand the dynamics of composite […] #### Special Right Triangles: Types, Formulas, with Solved Examples.

Learn all about special right triangles- their types, formulas, and examples explained in detail for a better understanding. What are the shortcut ratios for the side lengths of special right triangles 30 60 90 and 45 45 90? How are these ratios related to the Pythagorean theorem?  Right Angle Triangles A triangle with a ninety-degree […] #### Ways to Simplify Algebraic Expressions

Simplify algebraic expressions in Mathematics is a collection of various numeric expressions that multiple philosophers and historians have brought down. Talking of algebra, this branch of mathematics deals with the oldest concepts of mathematical sciences, geometry, and number theory. It is one of the earliest branches in the history of mathematics. The study of mathematical […]   