# Reflections

Reflections, a profound and introspective concept, encapsulate the thoughtful contemplation of one's experiences, ideas, and emotions. It is the mirror through which we navigate the tapestry of our lives, offering a unique lens to examine the past, present, and future. In its essence, reflections serve as a reservoir of wisdom, enabling individuals to gain insights, learn from their journey, and evolve. This introspective process not only fosters personal growth but also enhances our understanding of the world around us, making reflections a powerful tool for self-discovery and continuous improvement.

Questions

- A triangle has corners at #(6, 3 )#, ( 8, -2)#, and #(1, -1 )#. If the triangle is reflected across the x-axis, what will its new centroid be?
- A line segment goes from #(1 ,5 )# to #(7 ,6 )#. The line segment is dilated about #(1 ,2 )# by a factor of #3#. Then the line segment is reflected across the lines #x = 4# and #y=-2#, in that order. How far are the new endpoints form the origin?
- A triangle has corners at #(8, 3 )#, ( 2, -2)#, and #(7, -4 )#. If the triangle is reflected across the x-axis, what will its new centroid be?
- A line segment goes from #(5 ,2 )# to #(4 ,2 )#. The line segment is reflected across #x=-3#, reflected across #y=-5#, and then dilated about #(2 ,0 )# by a factor of #2#. How far are the new endpoints from the origin?
- A line segment goes from #(6 ,5 )# to #(7 ,3 )#. The line segment is dilated about #(2 ,1 )# by a factor of #3#. Then the line segment is reflected across the lines #x = 3# and #y=-4#, in that order. How far are the new endpoints form the origin?
- A triangle has corners at #(6, 4 )#, ( 2, 5)#, and #( 7, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?
- Point T(3, −8) is reflected across the x-axis. Which statements about T' are true?
- A line segment goes from #(3 ,4 )# to #(5 ,1 )#. The line segment is dilated about #(1 ,0 )# by a factor of #2#. Then the line segment is reflected across the lines #x=-2# and #y=2#, in that order. How far are the new endpoints from the origin?
- A triangle has corners at #(3, 7 )#, ( 5, -5)#, and #( 2, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?
- A line segment goes from #(2 ,3 )# to #(4 ,1 )#. The line segment is dilated about #(0 ,1 )# by a factor of #3#. Then the line segment is reflected across the lines #x=2# and #y=-1#, in that order. How far are the new endpoints from the origin?
- A triangle has corners at #(6, 7 )#, ( 2, -4)#, and #(9, -1 )#. If the triangle is reflected across the x-axis, what will its new centroid be?
- A line segment goes from #(1 ,2 )# to #(4 ,7 )#. The line segment is reflected across #x=6#, reflected across #y=-1#, and then dilated about #(1 ,1 )# by a factor of #2#. How far are the new endpoints from the origin?
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- 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?
- A line segment goes from #(1 ,2 )# to #(4 ,1 )#. The line segment is reflected across #x=-1#, reflected across #y=3#, and then dilated about #(2 ,2 )# by a factor of #3#. How far are the new endpoints from the origin?
- A triangle has corners at #(4, 3 )#, ( 7, -4)#, and #(6, -5 )#. If the triangle is reflected across the x-axis, what will its new centroid be?
- A triangle has corners at #(4, 4 )#, ( 3, -2)#, and #( 2, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?
- A line segment goes from #(4 ,1 )# to #(2 ,3 )#. The line segment is dilated about #(2 ,2 )# by a factor of #2#. Then the line segment is reflected across the lines #x = -2# and #y=4#, in that order. How far are the new endpoints form the origin?
- A line segment goes from #(3 ,1 )# to #(2 ,4 )#. The line segment is dilated about #(2 ,2 )# by a factor of #3#. Then the line segment is reflected across the lines #x = 4# and #y=-1#, in that order. How far are the new endpoints form the origin?
- A triangle has corners at #(4, 6 )#, ( 1 , -3)#, and #( 1 , -4)#. What will the new coordinates of the triangle be if it is reflected across the x-axis?