The vertices of a triangle are located at F(-4,-2), G (2,2), and H(0,-4). A sequence of transformations to triangle FGH results in triangle F'G'H', as shown below. Which sequence of transformations to triangle FGH results in triangle F'G'H'?
Answers
Answer:
Answer from: singlegirlforlife541
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.