HOW TO TRANSLATE A SHAPE BY A VECTOR

Translate the figures using given vector.

Example 1 :

Solution :

The first value is 4, means move the point 4 units right.

The second value is -2, means move the point 2 units down.

Example 2 :

Solution :

The first value is -3, means move the point 3 units left.

The second value is 2, means move the point 2 units up.

Example 3 :

Solution :

The first value is 0, means don't have to move horizontally.

The second value is -3, means move the point 3 units down.

Example 4 :

Solution :

The first value is 4, means move the point 4 units right.

The second value is 0, means don't have to move vertically.

Example 5 :

Solution :

The first value is -2, means move the point 2 units left.

The second value is -4, means move the point 4 units down.

Example 6 :

Solution :

The first value is -3, means move the point 3 units left.

The second value is 3, means move the point 3 units up.

Example 7 :

What translation vector moves Q to P ?

Solution :

By observing the vertex, moving 1 unit down and 3 units to the left we get the new rectangle.

So, the translation vector is

Example 8 :

Plot these coordinates to reveal a shape :

(-3, -1) (-3, -2) (1, -1) and (1, -2)

Translate the shape right 3 and up 3.

What are the coordinates of the new shape ?

Solution :

Given points are,  (-3, -1) (-3, -2) (1, -1) and (1, -2)

The shape is the rectangle, after doing the translation also we will get the same shape.

Translating each coordinate 3 units right and 3 units up, we get

• (x, y) ==> (x + 3, y + 3)
• (-3, -1) ==> (-3 + 3, -1 + 3) ==> (0, 2)
• (-3, -2) ==> (-3 + 3, -2 + 3) ==> (0, 1)
• (1, -1) ==> (1 + 3, -1 + 3) ==> (4, 2)
• (1, -2) ==> (1 + 3, -2 + 3) ==> (4, 1)

Example 9 :

Plot these coordinates to reveal a shape :

(2, 1) (4, 1) (0, -3) and (0, -1)

Translate the shape left 4 and up 1

What are the coordinates of the new shape ?

Solution :

Given points are, (2, 1) (4, 1) (0, -3) and (0, -1)

The shape is the trapezium, after doing the translation also we will get the same shape.

Translating each coordinate 4 units left and 1 unit up, we get

• (x, y) ==> (x - 4, y + 1)
• (2, 1) ==> (2 - 4, 1 + 1) ==> (-2, 2)
• (4, 1) ==> (4 - 4, 1 + 1) ==> (0, 2)
• (0, -1) ==> (0 - 4, -1 + 1) ==> (-4, 0)
• (0, -3) ==> (0 - 4, -3 + 1) ==> (-4, -2)

Example 10 :

Describe the positions and translations of the 2D shapes 

a) Starting coordinates

b) Translation

c) Finishing coordinates

Solution :

a) Starting coordinates are

(-2, 6) (-4, 1) and (0, 1)

b) Translation

9 units to the right and 11 units down

(x, y) ==> (x + 9, y - 11)

c) Finishing coordinates

• (-2, 6) ==> (-2 + 9, 6 - 11) ==> (7, -5)
• (-4, 1) ==> (-4 + 9, 1 - 11) ==> (5, -10) 
• (0, 1) ==> (0 + 9, 1 - 11) ==> (9, -10)

Example 11 :

This equilateral triangle is translated up 3.

Draw the triangle in its new position.

Solution :

The coordinates of the triangle given are 

(2, 3) (1, 1) and (3, 1)

After translating up for 3 units, we get

• (2, 3) ==> (2, 3 + 3) ==> (2, 6)
• (1, 1) ==> (1, 1 + 3) ==> (1, 4)
• (3, 1) ==> (3, 1 + 3) ==> (3, 4)

Example 12 :

The right angled triangle is translated right 3 units

Draw the triangle in its new position.

Solution :

The coordinates of the triangle given are 

(1, 2) (1, 6) and (3, 2)

After translating right for 3 units, we get

• (1, 2) ==> (1 + 3, 2) ==> (2, 6)
• (1, 6) ==> (1 + 3, 6) ==> (4, 6)
• (3, 2) ==> (3 + 3, 2) ==> (6, 2)