The last step is the rotation of y=x back to its original position that is counterclockwise at 45°.Įxample: A triangle ABC is given. After it reflection is done concerning x-axis. Reflection about line y=x: The object may be reflected about line y = x with the help of following transformation matrixįirst of all, the object is rotated at 45°. This is also called as half revolution about the origin.Ĥ. /rebates/2fhotmath2fhotmathhelp2ftopics2ftransformation-of-graphs-using-matrices-reflection&. In this value of x and y both will be reversed.
In the matrix of this transformation is given below
Reflection about an axis perpendicular to xy plane and passing through origin: The following figure shows the reflection about the y-axisģ. The object will lie another side of the y-axis. If point on a shape is reflected in the x-axis, the x-coordinate stays the same, but the y-coordinate changes sign. Here the values of x will be reversed, whereas the value of y will remain the same. Reflection about y-axis: The object can be reflected about y-axis with the help of following transformation matrix The object will lie another side of the x-axis.Ģ. Following figures shows the reflection of the object axis. Rules for Reflections on a Coordinate Plane Reflection across the x-axis Reflection across the y-axis (x, y)(-x,y) (x, y)V, x) Reflection across the line y. In this transformation value of x will remain same whereas the value of y will become negative. Reflection about x-axis: The object can be reflected about x-axis with the help of the following matrix