To find a reflection image of a point or a shape, there are some rules you can follow although it is not always possible to follow a rule.
First, let us start with all situations where you can just follow a rule to quickly find the location of the reflected image on the coordinate system.
Keep in mind that once you know how to find a reflection image for a point, you can easily find it for a shape. For example, if the shape has 3 points, just find the reflected image for all 3 points and then connect these points with a line.
Reflection of a point across the x-axis
The coordinate of point P is (3, 3) and the coordinate of the reflected image P' is (3, -3)
The coordinate of point A is (-2, 4) and the coordinate of the reflected image A' is (-2, -4)
What do you notice about the x-coordinate and y-coordinate of the preimage and image?
We see that the x-coordinate of the preimage stays the same, but the y-coordinate of the image is the opposite of the y-coordinate of the preimage.
In general, when reflecting a point across the x-axis, if the coordinate of the preimage is (x , y), then the coordinate of the reflected image is (x , -y)
Reflection of a point across the y-axis
The coordinate of point P is (-4, 3) and the coordinate of the reflected image P' is (4, 3)
The coordinate of point A is (2, -4) and the coordinate of the reflected image A' is (-2, -4)
What do you notice about the x-coordinate and y-coordinate of the preimage and image?
We see that the y-coordinate of the preimage stays the same, but the x-coordinate of the image is the opposite of the x-coordinate of the preimage.
In general, when reflecting a point across the y-axis, if the coordinate of the preimage is (x , y), then the coordinate of the reflected image is (-x , y)
Reflection of a point across the line y = x
The coordinate of point P is (1, 4) and the coordinate of the reflected image P' is (4, 1)
The coordinate of point A is (-5, -2) and the coordinate of the reflected image A' is (-2, -5)
Just swap the x-coordinate with the y-coordinate
In general, when reflecting a point across the line y = x, if the coordinate of the preimage is (x , y), then the coordinate of the reflected image is (y, x)
Reflection of a point across the line y = -x
The coordinate of point P is (2, 4) and the coordinate of the reflected image P' is (-4, -2)
The coordinate of point A is (4, -1) and the coordinate of the reflected image A' is (1, -4)
Therefore, swap the x-coordinate with the y-coordinate and then take the opposite of both coordinates.
In general, when reflecting a point across the line y = -x, if the coordinate of the preimage is (x , y), then the coordinate of the reflected image is (-y, -x)
The coordinate of point P is (5, 2) and the coordinate of the reflected image P' is (-5, -2)
The coordinate of point A is (-2, 3) and the coordinate of the reflected image A' is (2, -3)
Just take the opposite of both coordinates.
In general, when reflecting a point in the origin, if the coordinate of the preimage is (x , y), then the coordinate of the reflected image is (-x, -y)
When reflecting a point across any line, just keep this mind. The distance between the point and the line and the reflected point and the line is exactly the same.
When reflecting a point A in any point P, just keep this mind these two things.
The distance between point A and point P and the reflected point A' and point P is exactly the same.
Point P, the reflected point A' and point A are colinear.
Sep 01, 18 04:07 PM
These heart of algebra questions will help you prepare to take the math portion of the SAT
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.
Sep 01, 18 04:07 PM
These heart of algebra questions will help you prepare to take the math portion of the SAT
Our Top Pages
Formula for percentage
Compatible numbers
Basic math test
Basic math formulas
Types of angles
Math problem solver
Algebra word problems
Surface area of a cube
Finding the average
Scale drawings
Everything you need to prepare for an important exam!
K-12 tests, GED math test, basic math tests, geometry tests, algebra tests.
Real Life Math Skills
Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.