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3 years ago

△XYZ is mapped to △X'Y'Z' using the rules (x, y)→(x+5, y−3) followed by (x, y)→(−x, −y) .

Mathematics

1 answer:

Yuri [45]3 years ago

5 0

Given that △XYZ is mapped to △X'Y'Z' using the rules (x, y)→(x+5, y−3) followed by (x, y)→(−x, −y) .

We know that (x,y) => (x+h,y+k) type operation represents translation so rule (x, y)→(x+5, y−3) will cause translation.

We know that (x,y) => (-x,-y) type operation represents rotation about origin so rule (x, y)→(−x, −y) will cause rotation.

So combining both results and comparing with given choices. we find that only 1st choice "△XYZ is congruent to △X'Y'Z' because the rules represent a translation followed by a rotation, which is a sequence of rigid motions."

is correct.

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Step-by-step explanation:

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Pyramid A has a triangular base where each side measures 4 units and a volume of 36 cubic units. Pyramid B has the same height,

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Answer:

The volume of pyramid B is 81 cubic units

Step-by-step explanation:

Given

Pyramid A

$s = 4$ -- base sides

$V = 36$ -- Volume

Pyramid B

$s = 6$ --- base sides

Required

Determine the volume of pyramid B [Missing from the question]

From the question, we understand that both pyramids are equilateral triangular pyramids.

The volume is calculated as:

$V = \frac{1}{3} * B * h$

Where B represents the area of the base equilateral triangle, and it is calculated as:

$B = \frac{1}{2} * s^2 * sin(60)$

Where s represents the side lengths

First, we calculate the height of pyramid A

For Pyramid A, the base area is:

$B = \frac{1}{2} * s^2 * sin(60)$

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$B = \frac{1}{2} * 16 * \frac{\sqrt 3}{2}$

$B = 4\sqrt 3$

The height is calculated from:

$V = \frac{1}{3} * B * h$

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To calculate the volume of pyramid B, we make use of:

$V = \frac{1}{3} * B * h$

Since the heights of both pyramids are the same, we can make use of:

$h = \frac{27}{\sqrt 3}$

The base area B, is then calculated as:

$B = \frac{1}{2} * s^2 * sin(60)$

Where

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So:

$B = \frac{1}{2} * 6^2 * sin(60)$

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$B = 9\sqrt 3$

So:

$V = \frac{1}{3} * B * h$

Where

$B = 9\sqrt 3$ and $h = \frac{27}{\sqrt 3}$

$V = \frac{1}{3} * 9\sqrt 3 * \frac{27}{\sqrt 3}$

$V = \frac{1}{3} * 9 * 27$

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