Solving Vertical Reflection

The vertical reflection is usually a transformation that can be performed over a point or a line.

In vertical reflection we transform all points of an object to an another point which is to the equal length of the opposite side of a vertical line.

This produce a general rotation of straight angle (180°) that is  half turn along the axes.

Solving Vertical Reflection : Description

The vertical reflection flips the image or a given object across a given line x = y + c, c=variable. The new object is a vertically reflected object of the original given object.

Solving vertical reflection follow the given steps :

Step 1: In this step, we have to determine the distance from the coordinates of the object to the given horizontal line (y = x + c)

Step 2: To plot the  reflected coordinates on the vertically opposite side of the given horizontal line from the equal distance.

Step 3: Join all the new coordinates to get the new object .
Solving Vertical Reflection : Examples

Given is a triangle whose coordinates are P(x, y), Q(x, y), R(x, y).It is transformed with the help of vertical reflection, that is with respect to the horizontal line.

Solution:

Step 1: Draw the triangle object as per the given co-ordinates are P, Q, R in the X-Y plane.


Step 2:   Draw the horizontal line of that triangle PQR, and draw the vertical line from each co-ordinates of  given triangular object. Measure the distance from each point of each vertical lines are y1, y2, y3.


Step 3: Plot the vertically reflected  points are A', B', C', are at the  same vertical distance from the horizontal  line


Step 4:  Now, join the vertically reflected points  A', B', C'. We get the vertically reflected triangle.


Step 5:  This is the vertical reflection of the given triangle.

Solving Vertical Reflection : Practice Problems

Problem  : Perform vertical reflection to a given square having points A( x1,y1) B(x2,y2) c(x3,y3) and d(x4,y4). specify the new coordinates of the square after reflection.