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Tell weather the dilation is a reduction or an enlargement. Then find the scale factor
1 answer:
An image of dilation is given. It is required to determine if the dilation is an enlargement or a reduction and then find the scale factor.
Notice that the center of dilation is point O.
Notice also that point P is on the vertex of the pre-image and point P' is on the vertex of the image.
Since the pre-image is a smaller triangle than the image, it follows that the dilation is an enlargement.
The scale factor is the ratio of the distance of corresponding vertices to the center of dilation.
It follows that the scale factor is:
The scale factor is 3/2.
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Answer:
Around 5.5 square meters
Step-by-step explanation:
You can start by finding the area of the segment. Since the rest of the circle that is not in the segment is 240 degrees, the segment is 120 degrees or a third of the circle. You can therefore find the area of that segment with the formula square meters. Now, you need to find the area of the triangle inside the sector. This is more difficult than last time, because it is not a 90 degree angle. However, you can solve this by dividing this triangle into two 30-60-90 triangles, which you know how to find the ratio of sides for. In a 30-60-90 triangle, the hypotenuse is twice the length of the smallest leg, and the larger leg is
times larger than the smaller leg. In this case, these dimensions are a base of
for the smaller leg and
for the larger leg, or the base. Using the triangle area formula and multiplying by 2 (because remember, we divided the big triangle in half), you get
square meters. Subtracting this from the area of the segment, you get about 5.5 square meters. Hope this helps!