Online Translation of the Point Calculator
How to Use the ‘Translation of the Point' Calculator?
Follow the steps below to use the translation of the point calculator:
Step 1: Toggle and select the option of your choice as ‘single translation’ or ‘composition translation’.
Step 2: Enter the original point coordinates in the input box.
Step 3: Enter the value or units for the translation and also, select the direction for both the x-axis and y-axis. In case of composition translation enter the second translation units and diffraction as well.
Step 4: Click on the ‘Solve’ button to obtain the coordinates of the point after the translation. In composition translation coordinates after the first as well as the second translation can be calculated.
Step 5: Click on the ‘Show steps’ button to see the translation using the coordinate plane.
Step 6: Click on the button to enter new inputs and start again.
Step 7: Click on the ‘Example’ button to play with different random input values.
Step 8: Click on the ‘Explore’ button to drag and position the point on the coordinate plane. With the use of sliders it can be
translated for various units.
Step 9: When on the ‘Explore’ page, the arrows show the direction of translation along the x-axis and y-axis.
Step 10: When on the ‘Explore’ page, click on the ‘Calculate’ button if you want to go back to the calculator.
What is the Translation of a Point?
Translation is a specific form of transformation on the coordinate plane where size of the point or geometrical shape remains the same but only the position changes. The point or the figure can be moved upward, downward, right, left or in more than one direction along the x-axis and y- axis in the coordinate system.
How do we find the Coordinates of an Translated Point?
Consider a point A (x,y)
The following rules are used to find the coordinates:
- A movement of a units on the right = A (x+a,y)
- A movement of a units on the left = A (x-a,y)
- A movement of b units up = A (x,y+b)
- A movement of b units down = A (x,y-b)
To conclude,
When a point A(x,y) is translated along both x-axis and y axis
The translated point is A'(x ± a, y ± b).
When composition translation of a point A(x,y) is done using the two movements ⟨±a, ±b⟩ and ⟨±c, ±d⟩
The translated point is A”(x ± a ± c,y ± b ± d).
Solved Examples:
Example 1: Translate a point A(3,5)using the movement 5 units right and 1 units down.
Solution:
First plot the point A and then move it 5 units right and 1 units down or + 5 units along the x-axis and -1 units along the y-axis.
Given the rule for the translation is A'(x a,y b)
Hence, A(3,5) becomes A’(3+ (+5), 5+(-1)) = A’(8,4)
Example 2: Translate a point A(3, 3)using the movement 6 units left.
Solution:
First plot the point A and then move it 6 units left or – 6 units along the x-axis
A(3,3) becomes A’(3+ (-6), 3+(0)) = A’(-3,3)
Example 3: Translate a point A(15,-4)using the movement 8 units down.
Solution:
First plot the point A and then move it 8 units down or – 8 units along the y-axis
A(15,-4) becomes A’(15+ (0), -4+(-8)) = A’(15,-12)
Example 4: Translate the point A(-8,5) using composition translation of (5,-2) and then (-4,-2).
Solution:
Step 1: First plot A and move it 5 units right and 2 units down.
Given the rule for the translation is A'(x a,y b)
Here,
A (-8, 5) becomes A'(-8+(+5), 5+ (-2)) = A'(-3 ,3)
Step 2: Now useA'(-3 ,3) to move it 4 units left and 2 units down.
Given the rule for the second translation is A”(x ± c,y ± d)
A’(-3,3) becomes A” (-3 +(-4),3 +(-2)) = A”(-7,1)
When a figure or shape is made to move in the direction(s) right, left, up or down leads to its transformation mathematically. This specific form of transformation which changes only leads to movement but no rotation, reflection or change of size is termed as translation.
A translation that moves a shape left, right, up, or down or in more than one direction along the x-axis and y-axis in the coordinate plane falls in the category of translation. However, any transformation involving turn, rotation, reflection, or change in size does not qualify for translation. The translated shapes (or the image) are the same size as the original shape, indicating that they are congruent.
- Sliding a cartoon box from one corner to another
- A child sliding on the slide swing
- Moving and keeping a glass from one cabinet to another