# A triangle has corners at #(2, 5 )#, #( 1, 3 )#, and #( 4 , 2 )#. If the triangle is dilated by # 7 x# around #(1, 3)#, what will the new coordinates of its corners be?

Simply multiply the coordinates by the scaling factor, in this case 7.

(14, 35), (7, 21) and (28, 14)

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To dilate a triangle by a factor of 7 around the point (1, 3), we'll use the dilation formula:

New_x = center_x + dilation_factor * (original_x - center_x) New_y = center_y + dilation_factor * (original_y - center_y)

For the point (2, 5): New_x = 1 + 7 * (2 - 1) = 8 New_y = 3 + 7 * (5 - 3) = 17

For the point (1, 3): New_x = 1 + 7 * (1 - 1) = 1 New_y = 3 + 7 * (3 - 3) = 3

For the point (4, 2): New_x = 1 + 7 * (4 - 1) = 22 New_y = 3 + 7 * (2 - 3) = -4

So, the new coordinates of the triangle's corners after dilation are: (8, 17), (1, 3), and (22, -4).

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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 line segment has endpoints at #(7 ,5 )# and #(2 ,6)#. If the line segment is rotated about the origin by #(pi )/2 #, translated vertically by #3 #, and reflected about the x-axis, what will the line segment's new endpoints be?
- Point A is at #(-3 ,-4 )# and point B is at #(-5 ,-8 )#. 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?
- A triangle has corners at #(9 ,-5 )#, #(-2 ,-1 )#, and #(3 ,-4 )#. If the triangle is dilated by a factor of #2/5 # about point #(1 ,4 ), how far will its centroid move?
- A triangle has corners at #(4, 6 )#, ( 1 , 7)#, and #( 3, -4)#. If the triangle is reflected across the x-axis, what will its new centroid be?
- A line segment with endpoints at #(-1 , -9)# and #(3, -5 )# is rotated clockwise by #pi/2#. What are the new endpoints of the line segment?

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