Geometry Reflections

In geometric, the determination of reflection of a point in a line translation is performed only through a given point or line. In reflection of a point in a line, the basic ideas of reflection are the transformation of a point to a reflected point that is the equal length of the opposite side of a  line. The transformation of  reflections in two right angular axes produce a rotation of straight angle (180°), that is a half turn.

Reflection of a point:

Reflection:

The reflection is the "flip or mirror image" of it over a line.  So, the actual and mirror images are identical to each other.

The two very common reflections of polygons are given by

Horizontal reflections.

Vertical reflections.

The colored vertices used for each of the triangle.  The line of reflection is halfway from both red points, blue points, and green points. The line of reflection is directly in the center of both points.

Reflection of  a point in a line to describe the X-axis is consider the mirror line or axis of reflection. Therefore, we change the given geometric object point  into x = x  and y = -y.

geometry reflections

Reflection of  a point in a line to describe the Y-axis is consider the mirror line or axis of reflection.. Therefore, we change the given geometric object point  into x = -x  and y = y.

geometry reflections

Reflection Example:

We take a shape of triangle, Learn horizontal reflection assists, the transformation of the geometric triangle of co-ordinates are P, Q, and R. It is transformed by using the horizontal reflection, that is the horizontal line y = x.

Solution:

Step 1: To draw the triangle object from the given co-ordinates are P, Q, and R in the X-Y plane.

geometry reflections

Step 2:  To draw the horizontal line or mirror line of that triangle PQR, and draw the perpendicular line to the horizontal line or mirror line from each co-ordinates of  given triangular object. And then measure the distance of each perpendicular lines are y1, y2, y3.

geometry reflections

Step 3:  To plot the mirrored points are P', Q', R', the same vertical distance from the horizontal line or mirror line.

geometry reflections

Step 4:  To join the plotted points P', Q', R'. We get the horizontally reflected triangular object.

geometry reflections

Step 5:   This is required horizontal reflections of triangular object.

Horizontal reflection of X- axis:

Horizontal reflection assist that concepts to describe the x-axis are considering the mirror line. Then change all the coordinates of the given geometric object into the x = x and y = -y. For example,

geometry reflections