Question

The graph shows the dilation of ΔABC with the origin as its center. Which rule describes this transformation? A) (x, y) → (2x, 2y) B) (x, y) → (0.5x, 0.5y) C) (x, y) → (x + 2, y +2) D) (x, y) → (x - 2, y - 2)

Answer 1

Note: Since, you have not added the graph. So, I will give you a general overview of the concept of dilation, the understanding of which will make you clear your concept.

Step-by-step explanation:

We know that a dilation is the kind of transformation which produces an image which has the same shape as the original object, but having a different size.

Here are some key factors regarding dilation:

• Enlargement occurs when a dilation does create a larger image.

• Reduction occurs when a dilation does create a smaller image.

• A dilation shrinks or stretches the original object.
• If the scale factor > 1, the image will be a stretch (enlargement)
• If the scale factor is between 0 and 1, the image will be shrunk (reduction)
• If the scale factor = 1, the original object and the image will be congruent

Here is the impact of dilation when (x, y) → (2x, 2y):

• Dilation with scale factor 2, will have the rule as (x, y) → (2x, 2y). The image will be a stretch (enlargement) as the scale factor > 1.
• The location of the new coordinates of the image can be obtained by multiplying the coordinates of the original figure by 2.

For example, the coordinates of the image of a point A(4, 8) will be A'(2×4, 2×8) or A'(8, 16) after the dilation of scale 2 at the origin.

Here is the impact of dilation when (x, y) → (0.5x, 0.5y):

• Dilation with scale factor 0.5, will have the rule as (x, y) → (0.5x, 0.5y). The image will be shrunk (reduction) as the scale factor < 1.
• The location of the new coordinates of the image can be obtained by multiplying the coordinates of the original figure by 0.5.

For example, the coordinates of the image of a point A(4, 8) will be A'(0.5×4, 0.5×8) or A'(2, 4) after the dilation of scale 0.5 at the origin.

Keywords: dilation, transformation, enlargement, reduction

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