# A line segment has endpoints at #(5 ,6 )# and #(7 , 3)#. The line segment is dilated by a factor of #2 # around #(4 , 2)#. What are the new endpoints and length of the line segment?

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The new endpoints of the line segment after dilation by a factor of 2 around (4, 2) are (3, 10) and (5, -1). The length of the line segment is sqrt(61) units.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A triangle has corners at #(0, 5 )#, ( 1, -2)#, and #(7, -4 )#. If the triangle is reflected across the x-axis, what will its new centroid be?
- Circle A has a radius of #3 # and a center of #(3 ,2 )#. Circle B has a radius of #1 # and a center of #(4 ,7 )#. If circle B is translated by #<2 ,-1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- How should I do this question that is in the image below?33
- A triangle as corners at #(3 ,5 )#, #(5 ,2)#, and #(9 ,4)#. If the triangle is dilated by a factor of #4 # about #(1 ,9), how far will its centroid move?
- Which single transformation that would have the same result as the two transformations (a) rotation by #180^@# about origin and (b) reflection in #y#-axis?

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