Pentagon CDEFG is shown on the coordinate plane. Pentagon CDEFG is translated 7 units up and 5 units left, resulting in C'D'E'F'
1 answer:
Answer:
The length of line segment FG is equal to the length of F'G'
The perimeter of pentagon CDEFG is equal to the perimeter of pentagon C'D'E'F'G.
Step-by-step explanation:
Given
CDEFG and C'D'E'F'G
Translation: 7 units up and 5 units left
Solving (a): Segment FG and F'G'
When a shape is translated, the resulting image will have the same lengths as the original image (i.e, translation does not change measurements)
Hence:
Solving (b): Perimeter CDEFG and C'D'EF'G'
In (a), we established that lengths do not change during translation;
Hence:
The perimeter of the CDEFG and C'D'EF'G' will remain the same
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So since the vertex falls onto the axis of symmetry, we can just solve for that to get the x-coordinate of both equations. The equation for the axis of symmetry is , with b = x coefficient and a = x^2 coefficient. Our equations can be solved as such:
y = 2x^2 − 4x + 12:
y = 4x^2 + 8x + 3:
In short, the vertex x-coordinate's of y = 2x^2 − 4x + 12 is 1 while the vertex's x-coordinate of y = 4x^2 + 8x + 3 is -1.