Question

Which describes how triangle FGH could be transformed to triangle F prime G prime H prime in two steps? On a coordinate plane, triangle F G H has points (negative 2, 1), (negative 3, 3), (0, 1). Triangle F prime G prime H prime has points (negative 8, negative 4), (negative 12, negative 12), (0, negative 4). 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 factor of 4 and then a reflection across the x-axis

Explanation:

1. Vertices of triangle FGH:

• F: (-2,1)
• G: (-3,3)
• H: (0,1)

2. Vertices of triangle F'G'H':

• F': (-8,-4)
• G': (-12,-12)
• H': (0, -4)

3. Solution:

Look at the coordinates of the point H and H': to transform (0,1) to (0,-4) you can muliply each coordinate by 4 and then change the y-coordinate from 4 to -4. That is a dilation by a scale factor of 4 and a reflection across the x-axis. This is the proof:

• Rule for a dilation by a scale factor of 4: (x,y) → 4(x,y)

       (0,1) → 4(0,1) = (0,4)

• Rule for a reflection across the x-axis:{ (x,y) → (x, -y)

        (0,4) → (0,-4)

Verfiy the transformations of the other vertices with the same rule:

• Dilation by a scale factor of 4: multiply each coordinate by 4

       4(-2,1) → (-8,4)

       4(-3,3) → (-12,12)

• Relfection across the x-axis: keep the x-coordinate and negate the y-coordinate

        (-8,4) → (-8,-4) ⇒ F'

        (-12,12) → (-12,-12) ⇒ G'

Therefore, the three points follow the rules for a dilation by a scale factor of 4 and then a reflection across the x-axis.

Answer 2

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

Step-by-step explanation: