Question

c) translating shapes
sometimes you are asked to translate a shape on a grid. to do this, you need to translate each point of the shape and then join them up. make sure that each point moves the same distance and in the same direction.

• point a is translated 2 units right and 3 units up to a
• point b is translated 2 units right and 3 units up to b
• point c is translated 2 units right and 3 units up to c

activity 4

1. draw the image of region a after each of the following translations:

a) a is translated 2 units right and 3 units up to b
b) a is translated (5; 0) to c
c) a is translated (-4; -5) to d

Explanation:

Part (a)

Step 1: Identify vertices of A

First, find the coordinates of each vertex of region A. Let's assume the vertices of A are, for example, \( (1,2) \), \( (2,0) \), \( (4,-1) \) (from the grid).

Step 2: Apply translation (2 right, 3 up)

For a point \( (x,y) \), translating 2 units right means \( x + 2 \), and 3 units up means \( y + 3 \).

• For \( (1,2) \): New coordinates \( (1 + 2, 2 + 3) = (3,5) \)
• For \( (2,0) \): New coordinates \( (2 + 2, 0 + 3) = (4,3) \)
• For \( (4,-1) \): New coordinates \( (4 + 2, -1 + 3) = (6,2) \)

Step 3: Draw the new shape

Plot the new points \( (3,5) \), \( (4,3) \), \( (6,2) \) and connect them to form region B.

Part (b)

Step 1: Identify vertices of A

Using the same vertices as in part (a): \( (1,2) \), \( (2,0) \), \( (4,-1) \).

Step 2: Apply translation \( (5,0) \)

A translation \( (5,0) \) means 5 units right (x - coordinate + 5) and 0 units up/down (y - coordinate remains).

• For \( (1,2) \): New coordinates \( (1 + 5, 2 + 0) = (6,2) \)
• For \( (2,0) \): New coordinates \( (2 + 5, 0 + 0) = (7,0) \)
• For \( (4,-1) \): New coordinates \( (4 + 5, -1 + 0) = (9,-1) \)

Step 3: Draw the new shape

Plot the new points \( (6,2) \), \( (7,0) \), \( (9,-1) \) and connect them to form region C.

Part (c)

Step 1: Identify vertices of A

Using the same vertices as in part (a): \( (1,2) \), \( (2,0) \), \( (4,-1) \).

Step 2: Apply translation \( (-4,-5) \)

A translation \( (-4,-5) \) means 4 units left (x - coordinate - 4) and 5 units down (y - coordinate - 5).

• For \( (1,2) \): New coordinates \( (1 - 4, 2 - 5) = (-3,-3) \)
• For \( (2,0) \): New coordinates \( (2 - 4, 0 - 5) = (-2,-5) \)
• For \( (4,-1) \): New coordinates \( (4 - 4, -1 - 5) = (0,-6) \)

Step 3: Draw the new shape

Plot the new points \( (-3,-3) \), \( (-2,-5) \), \( (0,-6) \) and connect them to form region D.

Answer:

(Drawing Instructions):

• Part (a) (B): Translate each vertex of A 2 right, 3 up. Plot and connect.
• Part (b) (C): Translate each vertex of A 5 right, 0 up/down. Plot and connect.
• Part (c) (D): Translate each vertex of A 4 left, 5 down. Plot and connect.

(Note: Actual drawing requires using the grid to plot the calculated coordinates for each vertex of A after translation.)