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KonstantinChe [14]
3 years ago
6

What are the coordinates of the triangle after a dilation with a scale factor of 1/2? Center it at (-3, 0) .

Mathematics
1 answer:
algol133 years ago
5 0
On the graph, the distance from each point to the center of dilation is cut in half.

The vertices become ...
   (-5,4) ⇒ (-4, 2)
   (3, 8) ⇒ (0, 4)
   (5, 4) ⇒ (1, 2)

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Consider the vectors a =3i +j −k, b =i +j +4k, c=i +3j +k, d =−i −3j +k, g =−3i −j +k. Which pairs (if any) of these vectors are
11111nata11111 [884]

Answer:

a and b are perpendicular to each other, as are b and d, b and g

Step-by-step explanation:

To check whether two vectors are perpendicular to each other, we need the angle between these vectors to be 90 degrees.

We can find the angle between to vectors a and b from the following relation:

The cosine of the angle \theta between two vectors is equal to the dot product of this vectors divided by the product of vector magnitude.

So

cos(\theta) = \frac{a.b}{|a||b|}

cos(90) = 0, so when the dot product between vectors a and b is 0, it means that these vectors are perpendicular to each other.

Now, for your exercise, let's compute the dot product between these vectors.

-----------

a.b = (3,1,-1).(1,1,4) = 3+1-4 = 0

So a and b are perpendicular to each other.

------------

a.c = (3,1,-1).(1,3,1) = 3+3-1 = 5

a and c are not perpendicular to each other.

--------------

a.d = (3,1,-1).(-1,-3,1) = -3-3-1 = -7

So not perpendicular

---------------

a.g = (3,1,-1).(-3,-1,1) = -9-1-1 = -11

Not

-----------------

b.c = (1,1,4).(1,3,1) = 1+3+4 = 8

Not

------------------

b.d = (1,1,4).(-1,-3,1) = -1 -3 +4 = 0

b.d = 0, so b and d are perpendicular to each other

--------------------

b.g = (1,1,4).(-3,-1,1) = -3-1+4 = 0

b.g = 0, perpendicular

---------------------

c.d = (1,3,1).(-1,-3,1) = -1-9+1 = -9

No

-----------------------

c.g = (1,3,1).(-3,-1,1) = -3-3+1 = -5

No

------------------------

d.g = (-1,-3,1).(-3,-1,1) = 3+3+1 = 7

No

7 0
3 years ago
Which shows two expressions that are equivalent to (Negative 7) (Negative 15) (Negative 5)? (Negative 7) (Negative 75) and (Nega
dimulka [17.4K]

Answer:

1 3 and 4

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
4 + 2x - 7 = 12<br><br> ?????
Rainbow [258]

Answer:

15/2

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
The figure shows a line graph and two shaded triangles that are similar:
BaLLatris [955]

Answer:

Answer is B

just do your work and proof the work and that will give u the right answer

4 0
3 years ago
Read 2 more answers
Which two values of x are roots of the polynomial below?
Julli [10]

Answer:

B. and C.

Step-by-step explanation:

1. Set the polynomial equal to zero:

x² + 5x + 7 = 0

2. Plug the given values of a, b, and c into the quadratic formula:

x=\frac{-5+-\sqrt{5^{2}-4(1)(7) } }{2(1)}

3. Solve the square root:

x=\frac{-5+-\sqrt{25-4(1)(7)} }{2(1)}

x=\frac{-5+-\sqrt{25-28} }{2(1)}

x=\frac{-5+-\sqrt{-3} }{2(1)}

4. Simplify the rest:

x=\frac{-5+-\sqrt{-3} }{2}

5. Separate the solutions:

x=\frac{-5+\sqrt{-3} }{2}  , x=\frac{-5-\sqrt{-3} }{2}

Thus, options B and C are the answers.

hope this helps!

4 0
2 years ago
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