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PLATO Course Math 8, Unit Activity Transformations: Preston says the sequence of transformations that maps triangle ABC onto triangle DEF is: rotate it 180 degrees about the origin, and then translate it up 7 units.

Chanel says the sequence of transformations that maps triangle ABC onto triangle DEF is: reflect it across the x-axis, then reflect it across the y-axis, and then translate it up 6 units and left 1 unit.

Complete a table to find the rule for the rotation, the coordinates of triangle ABC, and the coordinates of the rotated image, triangle A′B′C′. Please put the letter before the coordinates.

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24cmunier954go 24cmunier954go · Answer 1

Answer:

A (-4,5) B (-3,1) C (-5,2) D (3,1) E (2,5) F(4,4)

Step-by-step explanation:

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MrRoyalgo MrRoyalgo · Answer 2

Transformation involves changing the position of a shape.

The transformation rule is: [tex]\mathbf{(x,y) \to (-x - 1,-y + 6)}[/tex]

From the graph, we have the following points

[tex]\mathbf{A = (-4,5)}[/tex]

[tex]\mathbf{B = (-3,1)}[/tex]

[tex]\mathbf{C = (-5,2)}[/tex]

First, triangle ABC is reflected across the x and y axes.

So, we have:

[tex]\mathbf{(x,y) \to (-x,-y)}[/tex]

Next, the points are shifted up by 6 units, and left by 1 unit.

So, we have:

[tex]\mathbf{(x,y) \to (-x - 1,-y + 6)}[/tex]

Apply the above transformation rule on ABC, we have:

[tex]\mathbf{C = (4 - 1,-5 + 6) = (3,1)}[/tex]

[tex]\mathbf{D = (3 - 1,-1 + 6) = (2,5)}[/tex]

[tex]\mathbf{E = (5 - 1,-2 + 6) = (4,4)}[/tex]

Hence, the transformation rule is: [tex]\mathbf{(x,y) \to (-x - 1,-y + 6)}[/tex]

And the image of the transformation are:

[tex]\mathbf{D = (3,1)}[/tex] [tex]\mathbf{E = (2,5)}[/tex] [tex]\mathbf{F = (4,4)}[/tex]