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 X-Axis 

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 

Check your knowledge 

1. Reflection across x axis (4, 2) is (4, -2) 

2. Reflection across y axis (-2, 3) is (2, 3) 

3. Reflection at origin (3, 0) is (-3, 0) 

4. 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. 

5. 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. 

6. 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: