# A line segment has endpoints at #(3 ,2 )# and #(5 ,4 )#. The line segment is dilated by a factor of #4 # around #(1 ,3 )#. What are the new endpoints and length of the line segment?

By signing up, you agree to our Terms of Service and Privacy Policy

To find the new endpoints after dilation, we first calculate the distance between the center of dilation and each endpoint. Then, we multiply these distances by the dilation factor (4) to find the new distances. Finally, we add these new distances to the coordinates of the center of dilation to find the new endpoints.

Center of dilation: (1, 3)

Endpoint 1: (3, 2) Distance from center of dilation: √((1 - 3)^2 + (3 - 2)^2) = √((-2)^2 + (1)^2) = √(4 + 1) = √5 New distance: 4 * √5 = 4√5 New endpoint 1: (1 + 4√5, 3 + 4√5) ≈ (7.47, 7.47)

Endpoint 2: (5, 4) Distance from center of dilation: √((1 - 5)^2 + (3 - 4)^2) = √((-4)^2 + (-1)^2) = √(16 + 1) = √17 New distance: 4 * √17 = 4√17 New endpoint 2: (1 + 4√17, 3 + 4√17) ≈ (17.71, 17.71)

New endpoints: (7.47, 7.47) and (17.71, 17.71)

To find the length of the line segment, we use the distance formula between the new endpoints:

Length = √((17.71 - 7.47)^2 + (17.71 - 7.47)^2) Length ≈ √((10.24)^2 + (10.24)^2) Length ≈ √(104.86 + 104.86) Length ≈ √209.72 Length ≈ 14.49

The length of the dilated line segment is approximately 14.49 units.

By signing up, you agree to our Terms of Service and Privacy Policy

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 line segment has endpoints at #(8 ,5 )# and #(2 ,1 )#. If the line segment is rotated about the origin by #( 3 pi)/2 #, translated horizontally by # - 1 #, and reflected about the y-axis, what will the line segment's new endpoints be?
- Point A is at #(-2 ,-8 )# and point B is at #(-5 ,3 )#. Point A is rotated #pi/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
- Points A and B are at #(6 ,5 )# and #(7 ,8 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/2 # and dilated about point C by a factor of #2 #. If point A is now at point B, what are the coordinates of point C?
- Point A is at #(-1 ,-8 )# and point B is at #(-5 ,3 )#. Point A is rotated #pi/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
- Point A is at #(5 ,3 )# and point B is at #(-3 ,2 )#. Point A is rotated #pi/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7