9514 1404 393
Answer:
A rotation 90° CW followed by translation right 5 units.
Step-by-step explanation:
It is easier to choose the right composition of transformations if we know what your choices are.
Figure F has an orientation that is 90° CW from that of figure E, so a 90° CW or 270° CCW rotation could be one of the transformations.
Rotation about the origin will move the figure so that the acute angle is in a different quadrant. In order to return it to the same quadrant a translation is required. The amount of translation will depend on whether it comes before or after the rotation.
Possible sequence of motions are ...
- A rotation 90° CW followed by translation right 5 units
- Translation up 5 units followed by rotation 90° CW
Answer:
Step-by-step explanation:
Remark
There are many ways you can do this. You could, for example, prove this by using just one diagram and do the algebra for that one diagram. Or you could use both diagrams and equate them. I'll do the latter.
Left Diagram
c^2 + the 4 small triangles surrounding c^2 gives
c^2 + 4 * (1/2 * a * b)
Right Diagram
2 * a * b + a^2 + b^2
By the symmetry of the situation, you can find the area of the figures in each diagram. Since a in the left is equal to a on the right, and since b on the left = b on the right, the areas are equal.
Solution
c^2 + 4(1/2 a*b) = 2 * a * b + a^2 + b^2
c^2 + 2*a*b = 2* a * b + a^2 + b^2
c^2 = a^2 + b^2
Notice that the 2ab on the left cancels out with the 2ab on the right.
Answer:
2x + 3y - 5 = 0
Step-by-step explanation:
(4 , -1) & (-2,3)
![Slope =\frac{y_{2}-y_{1}}{x_{2}-x_1}}\\\\=\frac{3-[-1]}{-2-4}\\\\=\frac{3+1}{-6}\\\\=\frac{4}{-6}\\\\=\frac{-2}{3}](https://tex.z-dn.net/?f=Slope%20%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_1%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7B3-%5B-1%5D%7D%7B-2-4%7D%5C%5C%5C%5C%3D%5Cfrac%7B3%2B1%7D%7B-6%7D%5C%5C%5C%5C%3D%5Cfrac%7B4%7D%7B-6%7D%5C%5C%5C%5C%3D%5Cfrac%7B-2%7D%7B3%7D)
m = -2/3; (4 , -1)
y - y1 = m(x - x1)
![y - [-1]= \frac{-2}{3}(x-4)\\\\y + 1 =\frac{-2}{3}x -4*\frac{-2}{3}\\\\y + 1 =\frac{-2}{3}x+\frac{8}{3}](https://tex.z-dn.net/?f=y%20-%20%5B-1%5D%3D%20%5Cfrac%7B-2%7D%7B3%7D%28x-4%29%5C%5C%5C%5Cy%20%2B%201%20%3D%5Cfrac%7B-2%7D%7B3%7Dx%20-4%2A%5Cfrac%7B-2%7D%7B3%7D%5C%5C%5C%5Cy%20%2B%201%20%3D%5Cfrac%7B-2%7D%7B3%7Dx%2B%5Cfrac%7B8%7D%7B3%7D)
Multiply the equation by 3
3y + 3 = -2x + 8
3y = -2x + 8 - 3
3y = -2x + 5
2x + 3y - 5 = 0
19
Starting amount 5
Adding 6 and 8
5+6+8=19
Answer is attached ! Hope it helps
