What is the image of Q for a dilation with the center (0,0) and a scale factor of 0.5?
1 answer:
Answer: OPTION A.
Step-by-step explanation:
A dilation is defined as a transformation in which the Image (The figure obtained after the transformation) and the Pre-Image (The original figure before the transformation) have the same shape, but they have different sizes.
In this case you know that the dilation is centered at the origin and the scale factor is:
Therefore, the rule is the following:
You can identify in the figure attached that the point Q is:
Therefore, you must multiply its coordinates by the scale factor 0.5 in order to get its Image Q'. This is:
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Answer:
29.42 units
Step-by-step explanation:
<u>1) Find the perimeter around the semi-circle</u>
To do this, we find the circumference of the circle using the given diameter:
where d is the diameter
Plug in 6 as the diameter
Divide the circumference by 2
Therefore, the perimeter around the semi-circle is 3π units.
<u>2) Find the perimeter around the rest of the shape</u>
Although it's impossible to determine the lengths of the varied sides on the right side of the shape, we know that all of those <em>vertical</em> sides facing the right add up to 6. We also know that all of those <em>horizontal </em>sides facing up add up to 7. Please refer to the attached images.
Therefore, we add the following:
7+6+7
= 20
Therefore, the perimeter around that area of the shape is 20 units.
<u>3) Add the perimeter around the semi-circle and the perimeter around the rest of the shape</u>
Therefore, the perimeter of the shape is approximately 29.42 units.
I hope this helps!
