015: Rectangle homework
1 answer:
You might be interested in
Answer:
Rectangle ABCD was dilated by followed by a translation of 7 units right and 1 unit down.
Step-by-step explanation:
Rectangle A'B'C'D' is a dilated form of rectangle ABCD.
Followed by a translation, as shown in the figure attached.
For dilation,
Scale factor =
=
=
Therefore, rectangle ABCD was dilated with a scale factor of about the origin.
Coordinates of point A → (-10, 6)
Coordinates of point A' → (1, 2)
Coordinates of image of point A after dilation,
(x, y) → (kx, ky)
A(-10, 6) → A"(-5, 3)
Coordinates of point A" after translation of 'h' units to the right and 'k' units down.
(x, y) → (x + h, y - k)
A"(-5, 3) → A'[(-5 + h), (3 - k)]
By comparing the coordinates of A'[(1, 2) and (-5 + h, 3 - k)],
-5 + h = 2 ⇒ h = 7
3 - k = 2 ⇒ k = 1
Therefore, rectangle ABCD was dilated by followed by a translation of 7 units right and 1 unit down.
Answer:
The area between the two functions is approximately 1.333 units.
Step-by-step explanation:
If I understand your question correctly, you're looking for the area surrounded by the the line y = 2x and the parabola y = x², (as shown in the attached image).
To do this, we just need to take the integral of y = x², and subtract that from the area under y = 2x, within that range.
First we need to find where they intersect:
2x = x²
2 = x
So they intersect at (2, 4) and (0, 0)
Now we simply need to take the integrals of each, subtracting the parabola from the line (as the parabola will have lower values in that range):
So the correct answer is C, the area between the two functions is 4/3 units.
