Answer:
(b) (x, y) ⇒ (-x, y); (x, y) ⇒ (x + 1, y + 1)
Step-by-step explanation:
A graph shows the image is consistent with reflection over the y-axis
(x, y) ⇒ (-x, y)
and translation right 1, up 1
(x, y) ⇒ (x +1, y +1)
These transformations are listed in the second choice.
__
In the attachment, the original image is blue, the reflected image is purple, and the final translated image is red.
-65=6b-11
Add 11 to both sides to get rid of the -11 on the right side
-54=6b
Then divide both sides by six to find the value of b
-9=b
So b is -9
Answer:
33/16
Step-by-step explanation:
x = y⁴/8 + 1/(4y²), 1 ≤ y ≤ 2
dx/dy = y³/2 − 1/(2y³)
Arc length is:
s = ∫ ds
s = ∫ √(1 + (dx/dy)²) dy
s = ∫₁² √(1 + (y³/2 − 1/(2y³))²) dy
s = ∫₁² √(1 + y⁶/4 − ½ + 1/(4y⁶)) dy
s = ∫₁² √(½ + y⁶/4 + 1/(4y⁶)) dy
s = ∫₁² ½ √(2 + y⁶ + 1/y⁶) dy
s = ∫₁² ½ √(y³ + 1/y³)² dy
s = ∫₁² ½ (y³ + 1/y³) dy
s = ½ (y⁴/4 − 1/(2y²)) |₁²
s = ½ (16/4 − 1/8) − ½ (1/4 − 1/2)
s = 33/16
Dilation is a transformation of scaling that requires a center of scaling and a factor of scaling.
Similarity is a relationship between two figures when there is a special transformation that transforms one figure into another.
This transformation can include any combination of rotation, shift and dilation.
That's why a pair of a source and its image after dilation are similar, but not all similar figures can be connected by dilation. For instance, rotation and/or shift transform a figure into another, similar one to the original, but not related through dilation..
