Atriangle has verticals at b(-3,0), c(2,-1), d(-1,2). which transformation would produce an image with verticals b”(-2,1), c”(3,2), d”(0,-1)?

The triangle is reflected across the x-axis and then translated 1 unite to the right , 1 unit up

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) reflected across the x-axis

 then the new point = (x , -y)

- If point (x , y) reflected across the y-axis

 then the new point = (-x , y)

- If the point (x , y) translated horizontally to the right by h units

 then the new point = (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 then the new point = (x - h , y)

- If the point (x , y) translated vertically up by k units

 then the new point = (x , y + k)

- If the point (x , y) translated vertically down by k units

 then the new point = (x , y - k)

* Now lets solve the problem

- A triangle has three vertices

- The vertices are B (-3 , 0) , C(2 , -1) , D (-1 , 2)

- The images of the vertices are B" (-2 , 1) , C" (3 , 2) , D" (0 , -1)

 after two steps of transformations

- After comparing the points with their images we find

# The x-coordinates of the points are added by 1

∴ There is translation to the right

# The y-coordinates of the points not add or subtracted by the same

   number, that means there is a transformation before the translation

   for the y-coordinates

# The sign of y-coordinates of the points are changed , that means

   there is a reflection across the x-axis

∴ B' is (-3 , 0) , C' is (2 , 1) , D' is (-1 , -2)

- After comparing the 1st image with the 2nd images we find

# The x-coordinates of the points are added by 1 and the

   y-coordinates are add by 1

∴ B" is (-2 , 1) , C" is (3 , 2) , D" is (0 , -1)

- From all above

* The triangle is reflected across the x-axis and then translated 1 unite

  to the right , 1 unit up

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have

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step-by-step explanation:

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