Four Co-ordinates

Key Concept

• Translation
• Translation in a coordinate plane
• Describing translation

Translation 

What is translation? 

The translation is the movement of a figure from one place of a plane to another without changing the shape and size. It can move upward, downward, left or right in the coordinate plane. Translation changes the position, not the shape or size of the figure. 

ABC is the pre-image and A’B’C’ is the translated image or image of ABC. 

Pre-image is defined as the image of the object on the coordinate plane before translation.  

The object after translation is referred to as an image. 

1.6. _Understanding Translation 

The displacement or change in position of the image from one place to another in the coordinate plane. While translating, each point is moving equal units for each coordinate. The image can move horizontally and vertically. If it is moving horizontally, its x-coordinate is getting changed. If it is moving vertically, its y-coordinate is getting changed. When it moves horizontally to the right a units, then its x coordinate moves x + a units, and if it moves horizontally to the left units, then its x coordinate moves x-a units. If it moves vertically upwards b units, then its y coordinate moves y + b units and if it moves vertically downwards, then its y coordinate moves y-b units downwards. 

Here Black triangle QGZ is the pre-image, and Q’G’ Z’ is the translated image or the image. 

Q. Write a rule to describe each translation 

    Translation: 4 units right and 2 units upwards or translation (4, 2) 

Describing Translation 

Describe the translation from the pre-image to the image, X moves 8 units to the right, and Y moves 4 units down. In coordinate points, the translation can be represented as   

Q. Write a rule to describe the translation. 

      Translation 4 units up 

Q. Translation: (x, y) → (x-3, y+1)  

     The points in the pre-image is M(0, -3), J(1, 0), R(5, 0), H(2, -3) 

     Points in the image after translation M’(-3, -2),J’(-2, 1), R’(2, 1), H’(-1, -2) 

Exercise:

1. Translate the points (-4,5), 6 units to the right.
2. Translate 4 units right and 2 units up.

3. Write a rule for the translation.

4. Graph and label the polygon using the coordinates below and label the image created by the translation. A(-1,0), B (-6,1), C (-5,3) (x,y) → (x + 5, y + 2)

5. Use the translation (x,y) – (x + 4, y-8) i. What is the image of A(-1,3)? ii. What is the pre-image of B’ (12,7)?

6. The vertices of triangle ABC are A (-5, -6), B (-2,-9) and C (-4,1). Find the vertices of the image using translation. i. ii. (x,y) → (x+3, y) (x,y) + (x + 10, y +4)

Concept Map: 

What we have learnt:

• Translation
• Translation In a coordinate plane
• Understanding translation
• Describing translation