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andreyandreev [35.5K]

2 years ago

5

Point K is rotated 90°. The coordinate of the pre-image point K was (2, –6) and its image K’ is at the coordinate (−6, −2). Find

the direction of the rotation. The direction of rotation was .

1 answer:

umka21 [38]2 years ago

8 0

Answer:

Hello! The answer to your question will be below.

Step-by-step explanation:

The answer would be clockwise.

So point k was rotated 90 degrees clockwise.....

Review.....

Question:

Point K is rotated 90 degrees. The coordinate of the pre-image point K was (2,-6) and it’s image K’ is at the coordinate (-6,-2).Find the direction of the rotation.

THE DIRECTION OF THE ROTATION WAS CLOCKWISE.

Hope this helps! :)

⭐️Have a wonderful day!⭐️

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The equation:

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Find the distance between the point (-2, -3) and the line with the equation y=4-2/3x

otez555 [7]

Answer:

$D = \frac{25\sqrt{13}}{13}$

Step-by-step explanation:

Given

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Required

Determine the distance

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Write the above equation in standard form:

$Ax + By + C = 0$

So, we have:

$\frac{2}{3}x+y - 4 = 0$

By comparison:

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The distance is calculated using:

$D = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}$

Where:

$(x_1,y_1) = (-2,-3)$

$A = \frac{2}{3}$ $B = 1$ and $C = -4$

This gives:

$D = \frac{|\frac{2}{3} * (-2) + 1 * (-3) - 4|}{\sqrt{(\frac{2}{3})^2 + 1^2}}$

$D = \frac{|-\frac{4}{3} -3 - 4|}{\sqrt{\frac{4}{9} + 1}}$

Take LCM

$D = \frac{|\frac{-4-9-12}{3}|}{\sqrt{\frac{4+9}{9}}}$

$D = \frac{|\frac{-25}{3}|}{\sqrt{\frac{13}{9}}}$

$D = |\frac{-25}{3}|/\sqrt{\frac{13}{9}}$

$D = \frac{25}{3}/\sqrt{\frac{13}{9}}$

Split the square root

$D = \frac{25}{3}/\frac{\sqrt{13}}{\sqrt{9}}$

Change / to *

$D = \frac{25}{3}*\frac{\sqrt{9}}{\sqrt{13}}$

$D = \frac{25}{3}*\frac{3}{\sqrt{13}}$

$D = \frac{25}{\sqrt{13}}$

Rationalize

$D = \frac{25}{\sqrt{13}} * \frac{\sqrt{13}}{\sqrt{13}}$

$D = \frac{25\sqrt{13}}{13}$

Hence, the distance is:

$D = \frac{25\sqrt{13}}{13}$

4 0

2 years ago

A school chorus has 90 sixth-grade students and 75 seventh-grade students. The music director wants to make groups of performers

Tresset [83]

Answer:

The music director can form a total of 15 groups

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Sixth grade students = 90

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90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.

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The highest common factor of 75 and 90 is 15

Therefore, the music director can form a total of 15 groups

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2 years ago

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Answer:

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We can also express the relationship between x and y as:

y =

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3 years ago