Translation Math

In the previous post we have discussed about Symbolic Logic and In today's session we are going to discuss about Translation Math. In mathematics, to move a figure or a shape from one place to another we use translation. In this a figure in a plane can be move upward and downward, right, left or anywhere. It is a function that moves every point a constant distance in a particular direction. Suppose we move one point of a shape like Triangle, Square, Line, etc up to five unit in a particular direction by translation, then all the points will move by five unit in same direction. Thus only the position of the object changes but its size remains the same.

To understand better let us translate in the following graph:

The graph on the left side is translated to the graph on the right side.

The equation of the absolute value function of left hand side graph:

y = |x|.

When the function f(x) is translated ‘p’ units horizontally, then the argument of f(x) becomes x − p.

Thus as the origin is moved to (3, 4), the new equation by its translation is:

y − 4 = |x − 3|.

Let us have a rectangular on a graph with the points P(-4, 8), Q(1, 8), R(-4, 4), S(1, 4). To shift it by four unit downward we use the following steps:

As the figure is being translated by “four” unit in downward direction, there will be no changes in x- coordinate. (know more about Translation Math, here)

1. subtract by 4 in y coordinate, we get

P(-4, 8) after translation (x - 0, y – 4),

=> (-4 - 0, 8 – 5),

• (-4, 3)

2. For Q(1, 8) after translation, we get (x - 0, y - 4)

• (1 - 0, 8 - 5)
• (1, 3) translated coordinate.

3. For R(-4, 4) so, after translation (x - 0, y - 4)

=> (-4 - 0, 4 - 4)

=> (-4, 0) translated coordinate.

4. For S(1, 4), after translation,we get (x - 0, y - 4)

=> (1 - 0, 4 - 4)

=>(1, 0) translated coordinate.

So, translated figure coordinates will be points P(-4, 3), Q(1, 3), R(-4, 0), S(1, 0).

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