Question

Which describes how triangle FGH could be transformed to triangle F prime G prime H prime in two steps? Which identifies the transformation that occurred after the dilation?
a dilation by a scale factor of 3 and then a reflection across the x-axis
a dilation by a scale factor of 3 and then a 180 degrees rotation about the origin
a dilation by a scale factor of 4 and then a reflection across the x-axis
a dilation by a scale factor of 4 and then a 180 degrees rotation about the origin

Answer 1

Answer:

a dilation by a scale by a scale factor of 4 and then a reflection across the x-axis.

Step-by-step explanation:

In the image attached you can observe the original triangle and the transformed triangle.

Notice that transformed triangle is opposite to the original with respect to the x-axis, that means there was need a reflection across the x-axis to have that transformation.

Also, the triangle was dilated by a scale factor of 4, because each original coordinate is the fourth part of the transformed coordinates, for example, point F(-2, 1) was transformed to F'(-8,-4).

Therefore, the right answer is: a dilation by a scale factor of 4 and then a reflection across the x-axis.

Answer 2

Given : triangle FGH could be transformed to triangle F' , G',  H'   in two steps

To find : Which identifies the transformation that occurred after the dilation

a dilation by a scale factor of 3 and then a reflection across the x-axis

a dilation by a scale factor of 3 and then a 180 degrees rotation about the origin

a dilation by a scale factor of 4 and then a reflection across the x-axis

a dilation by a scale factor of 4 and then a 180 degrees rotation about the origin

Solution:

F = (-2 ,1 )    F' = (-8  , - 4)

G = (-3 , 3)   G' = (-12 ,  -12)

H = ( 0 , 1)    H'  = ( 0 , - 4)

Hence x' = 4x    and  y' = -4y

FH =  2 unit

F'H'  = 8 units

Scale of 4  

Reflection across x axis  - x remains a and y becomes -y

Hence reflection across x axis and dilation of 4

a dilation by a scale factor of 4 and then a reflection across the x-axis

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