GRAPHING ENLARGEMENTS

When a dilation in the coordinate plane has the origin as the center of dilation, we can find points on the dilated image by multiplying the x and y coordinates of the original figure by the scale factor.

For example, if the scale factor is 'k', the algebraic representation of the dilation is

(x, y) → (kx, ky)

For enlargements, k > 1.

Example 1 :

The triangle PQR shown on the grid is the pre-image. If the center of dilation is the origin and the scale factor is 3, graph the dilated image P'Q'R'.

Solution : 

Step 1 :

List the coordinates of the vertices of the pre image. 

P(1, 3), Q(3, 1) and R(1, 1)

Step 2 :

Since the scale factor is 3, the rule to get the coordinates of the vertices of the image is 

 (x, y) → (3x, 3y)

Step 3 :

List the coordinates of the vertices of the image. 

P(1, 3)  --->  P'(3, 9)

 Q(3, 1)  --->  Q'(9, 3)

R(1, 1)  --->  R'(3, 3)

Step 4 : 

Graph the image P'Q'R'.

Example 2 :

The rectangle JKLM shown on the grid is the pre-image. If the center of dilation is the origin and the scale factor is 2, graph the dilated image J'K'L'M'.

Solution : 

Step 1 :

List the coordinates of the vertices of the pre image. 

J(1, 1), K(3, 1), L(3, 4) and M(1, 4)

Step 2 :

Since the scale factor is 2, the rule to get the coordinates of the vertices of the image is 

 (x, y) → (2x, 2y)

Step 3 :

List the coordinates of the vertices of the image. 

J(1, 1)  --->  J'(2, 2)

 K(3, 1)  --->  K'(6, 2)

L(3, 4)  --->  L'(6, 8)

M(1, 4)  --->  M'(2, 8)

Step 4 : 

Graph the image J'K'L'M'.

Example 3 :

The triangle ABC shown on the grid is the pre-image. If the center of dilation is the origin and the scale factor is 3, graph the dilated image A'B'C'.

Solution : 

Step 1 :

List the coordinates of the vertices of the pre image. 

A(1, 3), B(3, 3) and C(1, 1)

Step 2 :

Since the scale factor is 3, the rule to get the coordinates of the vertices of the image is 

 (x, y) → (3x, 3y)

Step 3 :

List the coordinates of the vertices of the image. 

A(1, 3)  --->  A'(3, 9)

 B(3, 3)  --->  B'(9, 9)

C(1, 1)  --->  C'(3, 3)

Step 4 : 

Graph the image A'B'C'.

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.