What are the coordinates of (-4,-2) rotating 90° counterclockwise?
1 answer:
Answer:
(2, -4)
Step-by-step explanation:
The rotation of an object <u>turns</u> the object around a <u>fixed point</u> called the center of rotation.
A <u>rotation</u> of 90° counterclockwise means:
A 90° rotation counterclockwise with the origin (0, 0) as the center of rotation.
The rule for a counterclockwise rotation of 90° about the origin is:
(x, y) → (-y, x)
Therefore:
(-4, -2) → (2, -4)
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We are going to do this step by step:
Let's start with option A
A.
X = 25 and Y = 5/2
In this case, when X = 25 , then Y = 10 ,which is different to 5/2
B.
X = 14 , Y = 35
In case, when X = 14, then Y = 28/5, which is different to 35
C.
X = 40 , Y = 24
Similarly, in this case, when X = 40, then Y = 16, which is different to 24
D.
X = 10 , Y=4
Now, in this case, we can see that when X = 10, then Y = 4 which is the same as the given value of Y
E.
X = 50 , Y = 20
In this case, the values of Y are also the same.
F.
X = 30 , Y = 12
Again, in this case, the values of Y are the same, so the pair satisfies the equation.
In conclusion: options D, E and F satisfy the equation
The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.
Let the area be y .
Area = (base) × (height)
Base = 2x
Height = h
Let the area of the rectangular pens be y .
∴ y = 2xh
Perimeter of all the fencing = 4x+3h
∴ 4x+3h = 120
now we solve for h
3h = 120-4x
h = 40 - 4/3 x
Now we will substitute this value in the above first equation:
y = 2xh
or, y = 2x (40 - 4/3 x)
or, y = 80x - 8/3 x²
Now for the maximum area we have to find the first order differentiation of y
now,
dy /dx = 80 - 16/3 x
At dy/dx = 0 we get the value of x for which y is maximum.
80 - 16/3 x = 0
or, - 16/3 x = -80
or, x = 15 feet
Hence height = 40 - 4/3 x = 40 - 20 = 20feet
Maximum area = 2xh = 2×15×40 = 1200 square feet
The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.
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