<u><em>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.</em></u>
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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and get 31.40 cm squared