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Ira Lisetskai [31]
3 years ago
14

2. A triangular pyramid begins with these coordinates:

Mathematics
2 answers:
Bogdan [553]3 years ago
6 0
General rule for the reflection. r(x,y,z)= f(x,-y,z)

Results:
P: (0, - 5, 4)
Y: (-2, - 7, 4)
R: (0, - 7, 4)
A: (0, - 7, 6)

General rule for the translation: t(x,y,z) = r(x+2, y-4,z+3)

Result:

P: (0-2, -5+4 , 4-3) = (-2, -1, 1)
Y: (-2-2, - 7+4, 4-3) = (-4, -3, 1)
R: (0-2, - 7+4, 4-3) = (-2, -3, 1)
A: (0-2, - 7+4, 6-3) = (-2, -3, 3)


 

 


Allisa [31]3 years ago
4 0

Answer:

1)

(x,y,z) → (x,-y,z).

2)

P:(0,5,4) → P'(0,-5,4)

Y: (-2, 7, 4)  → Y'(-2,-7,4)

R: (0, 7, 4)  → R'(0,-7,4)

A: (0, 7, 6) → A'(0,-7,6)

3)

(x',y',z') → (x'-3,y'-2,z'+4).

4)

P:(0,5,4) → P"(-3,-7,8)

Y: (-2, 7, 4)  → Y"(-5,-9,8)

R: (0, 7, 4)  → R"(-3,-9,8)

A: (0, 7, 6) → A"(-3,-9,10).

Step-by-step explanation:

A triangular pyramid begins with these coordinates:

P: (0, 5, 4)

Y: (-2, 7, 4)

R: (0, 7, 4)

A: (0, 7, 6)

1)

The pyramid is reflected over the xz-plane.

so the rule of the reflection will be:

The points x,y,z are transformed to x,-y,z.

i.e. (x,y,z) → (x',y',z').

where (x'y'z')=(x,-y,z)

i.e. (x,y,z) → (x,-y,z)

2)

The coordinates of the points after reflection is:

P:(0,5,4) → P'(0,-5,4)

Y: (-2, 7, 4)  → Y'(-2,-7,4)

R: (0, 7, 4)  → R'(0,-7,4)

A: (0, 7, 6) → A'(0,-7,6)

3)

The general rule of translation is:

(x',y',z') → (x'-3,y'-2,z'+4).

4)

Hence, our point P,Y,R and A are given as:

P:(0,5,4) → P''(0-3,-5-2,4+4)=P"(-3,-7,8)

Y: (-2, 7, 4)  → Y''(-2-3,-7-2,4+4)=Y"(-5,-9,8)

R: (0, 7, 4)  → R''(0-3,-7-2,4+4)=R"(-3,-9,8)

A: (0, 7, 6) → A''(0-3,-7-2,6+4)=A"(-3,-9,10).

i.e.

P:(0,5,4) → P"(-3,-7,8)

Y: (-2, 7, 4)  → Y"(-5,-9,8)

R: (0, 7, 4)  → R"(-3,-9,8)

A: (0, 7, 6) → A"(-3,-9,10).

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Step-by-step explanation:

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6 0
2 years ago
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Find the diameter of the circle with the given circumference use 3.14 C=18
algol [13]
The formula for the circumference of a circle is pi * r * 2

First we solve for r (the radius)
pi*r*2 = C
pi*r*2 = 18

Divide 18 by 2
pi*r = 9

Then divide 9 by 3.14
pi= 9/3.14 which is 2.866

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3 0
3 years ago
A new park was designed to contain two circular gardens. Garden A has a diameter of 50 m, and garden B has a diameter of 70 m. T
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Answer:

5,811.95\  m^2 of fabric.

Step-by-step explanation:

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A=A_s+A_b\\\\=\pi r^2+\pi R^2\\\\=\pi(25^2+35^2)\\\\=1850\pi \ m^2\\\\=5811.95\ m^2

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5 0
3 years ago
Dorian is spreading mulch on his triangular flowerbed. If the base is 8 feet and the height is 6 feet. How many square feet of m
katovenus [111]

Answer:

24 square feet

Step-by-step explanation:

Given:

Dorian is spreading mulch on his triangular flowerbed.

The base is 8 feet.

The height is 6 feet.

Question asked:

How many square feet of mulch will he need for the flowerbed?

Solution:

The base of  triangular flowerbed = 8 feet.

The height of  triangular flowerbed = 6 feet.

now, to find how many square feet of mulch he will need for the flowerbed, we will find area of the triangular flowerbed:-

As we know:

Area\ of\ triangle=\frac{1}{2} \times base\times height

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Thus, 24 square feet of mulch he will need for the flowerbed.

8 0
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Simplify the expression 4^3+ 2(3 − 2). <br> 14 <br> 16 <br> 66 <br> 68
daser333 [38]

Answer:

66

Step-by-step explanation:

4^3=64

64+2(3-2)

64+6-4 =64+2.

64+2=66

5 0
3 years ago
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