# A line segment has endpoints at #(8 ,1 )# and #(7 ,5 )#. If the line segment is rotated about the origin by # pi #, translated horizontally by # - 2 #, and reflected about the x-axis, what will the line segment's new endpoints be?

(-10 , 1) and (-9 , 5)

Let's begin by naming the endpoints A(8 , 1) and B(7 , 5)

step 1 : A (8 , 1 ) → A' (-8 , -1) and B (7 , 5) → B'(-7 , -5)

step 2 : A'(-8 , -1) → A''(-10 , -1) and B'(-7 ,-5) → B''(-9 , -5)

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

step 3 : A'' (-10 , -1) → A'''(-10 , 1) and B''(-9 , -5) → B'''(-9 , 5)

hence new endpoints are (-10 , 1) and (-9 , 5)

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

The new endpoints of the line segment after it's rotated about the origin by ( \pi ), translated horizontally by -2, and reflected about the x-axis are: Endpoint 1: ((-5, -1)) Endpoint 2: ((-6, -5))

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.

- Points A and B are at #(9 ,2 )# and #(2 ,5 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/2 # and dilated about point C by a factor of #3 #. If point A is now at point B, what are the coordinates of point C?
- Points A and B are at #(8 ,3 )# and #(5 ,7 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/2 # and dilated about point C by a factor of #3 #. If point A is now at point B, what are the coordinates of point C?
- Points A and B are at #(2 ,6 )# and #(1 ,9 )#, respectively. Point A is rotated counterclockwise about the origin by #pi # and dilated about point C by a factor of #1/2 #. If point A is now at point B, what are the coordinates of point C?
- Points A and B are at #(4 ,6 )# and #(7 ,5 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/2 # and dilated about point C by a factor of #1/2 #. If point A is now at point B, what are the coordinates of point C?
- A triangle as corners at #(3 ,1)#, #(5 ,2)#, and #(9 ,4)#. If the triangle is dilated by a factor of #4 # about #(1 ,9), how far will its centroid move?

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