Co-Authored By:

##### Asked by: Gianpiero Zabalza-Irisarri

science space and astronomy# How do you translate points on a graph?

If asked to

**translate**a**point**(x+1,y+1), you move it to the right one unit because + on the x-axis goes to the right, and move it up one unit, because + on the y-axis goes up.

Similarly, you may ask, what is the formula for translation?

In the coordinate plane we can draw the **translation** if we know the direction and how far the figure should be moved. To **translate** the point P(x,y) , a units right and b units up, use P'(x+a,y+b) .

**transformation**takes whatever is the basic function f (x) and then "transforms" it (or "translates" it), which is a fancy way of saying that you change the formula a bit and thereby move the graph around. Moving the function down

**works**the same way; f (x) – b is f (x) moved down b units.

Hereof, what is an image point?

Reflection - of a **point** The given **point** P is "reflected" in the mirror and appears on the other side of the line an equal distance it. The reflection of the **point** P over the line is by convention named P' (pronounced "P prime") and is called the "**image**" of **point** P.

**The function translation / transformation rules:**

- f (x) + b shifts the function b units upward.
- f (x) – b shifts the function b units downward.
- f (x + b) shifts the function b units to the left.
- f (x – b) shifts the function b units to the right.
- –f (x) reflects the function in the x-axis (that is, upside-down).