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3 years ago

What is the complex formula for dilation with scale factor 2 and rotation by 90

Mathematics

1 answer:

zhuklara [117]3 years ago

7 0

Answer:

z' = 2iz +11 -2i

Step-by-step explanation:

Dilation multiplies each point by the scale factor. Rotation by 90° CCW is equivalent to multiplication by i.

When the center is not the origin, the transformation is applied to the difference from the center, then the result is added to the center.

z' = 2i(z -(3+4i)) + (3+4i)

Simplifying gives ...

z' = 2iz -6i +8 +3 +4i

z' = 2iz +11 -2i

_____

Check

For example, consider the point 1 unit east of the center of dilation/rotation. That point is z = 4+4i. Applying the transformation moves this point to ...

z' = 2i(4 +4i) +11 -2i = 8i -8 +11 -2i

z' = 3 +6i . . . . . 2 units north of the center of dilation/rotation

This is where it is expected to be after dilation by a scale factor of 2 and rotation 90° CCW.

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3rd question, I’m sorry guys but I was sick that’s why I didn’t attend school and the teacher said if I didn’t submit it by 5 ho

aniked [119]

Answer:

21. ΔUYZ Obtuse

22. ΔBCD Right or Rectangle

23. ΔADB Acute

24. ΔUXZ Acute

25. ΔUWZ Right or Rectangle

26. ΔUXY Equiangular and acute

Step-by-step explanation:

We need to classify each triangle by its angles.

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Obtuse: The inner angle A is obtuse (more than 90 degrees). The other 2 angles are acute.

ΔUYZ Obtuse The inner angle Y is obtuse (more than 90°).

ΔBCD Right or Rectangle The inner angle C is straight (90°).

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ΔUXZ Acute It has 3 acute angles (less than 90°).

ΔUWZ Right or Rectangle The inner angle W is straight (90°).

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3 0

3 years ago

so..my teacher NEEDS work from us so please don't put a random answer i need the work for that. thanks

nika2105 [10]

Answer:

Original Equation: s + 3 1/2 = 8 1/2

Subtract 3/12 from both sides: s + 3 1/2 - 3 1/2 = 8 1/2 - 3 1/2

Simplify: s = 5

So, A is the correct answer.

Let me know if this helps!

8 0

3 years ago

Six friends equally share a bag of popcorn. The bag contains 9 cups of popcorn. How many cups of popcorn should each friend get?

nadya68 [22]

Six friend =6
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7 0

3 years ago

Read 2 more answers

Show all work to identify the asymptotes and zero of the faction f(x) = 4x/x^2 - 16.

Reptile [31]

Answer:

asymptotes: x = -4, x = 4
zeros: x = 0

Step-by-step explanation:

The vertical asymptotes of the rational expression are the places where the denominator is zero:

x^2 -16 = 0

(x -4)(x +4) = 0 . . . . . true for x=4, x=-4

x = 4, x = -4 are the equations of the vertical asymptotes

The zeros of a rational expression are the places where the numerator is zero:

4x = 0

x = 0 . . . . . . divide by 4

5 0

3 years ago

A line is defined by the equation y = two-thirds x minus 6. The line passes through a point whose y-coordinate is 0. What is the

DedPeter [7]

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3 0

2 years ago