# A triangle has corners at #(3, 9 )#, ( 6, -5)#, and #( 4, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

The first step is to find the coordinates of the centroid.

Hence coords of centroid

Now under reflection in the x-axis a point (x,y) → (x , -y)

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The centroid of the original triangle is (4.333, 1). When the triangle is reflected across the x-axis, the new centroid will have the same x-coordinate but the y-coordinate will be negative, making the new centroid (4.333, -1).

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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 #(3, -5 )#, ( 2 , -1)#, and #( 4 , 3)#. What will the new coordinates of the triangle be if it is reflected across the x-axis?
- Point A is at #(4 ,1 )# and point B is at #(-6 ,-7 )#. Point A is rotated #(3pi)/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 #(1 ,3 )# and point B is at #(-7 ,-5 )#. 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?
- A line segment has endpoints at #(2 ,7 )# and #(5 ,4 )#. The line segment is dilated by a factor of #3 # around #(4 ,3 )#. What are the new endpoints and length of the line segment?
- A line segment has endpoints at #(4 ,7 )# and #(2 ,5 )#. The line segment is dilated by a factor of #4 # around #(3 ,3 )#. What are the new endpoints and length of the line segment?

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