Explain how you know a system of equations has

1 answer:

4 0

When they have no solutions, the lines are parlaell, or they have the same slope but different y intercept
example

3x+2y=2 and
3x+2y=4 are paralell
also
y=3x+2 and
y=3x+4 are also parlell, no solutions

infinite solutions are when they are the same line
they have the same slope and y intercept
to find out, simplify
3x+2y=4 and
6x+4y=8 are smae lien
also
y=3x+2 and
2y=6x+4 aer the same line

1 solution is when it is none of the above things
a normal thing, where the slopes are differnet
example
y=2x+2
y=3x+2

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Quadrilateral ABCD is dilated by a scale factor of 2 centered around (2, 2). Which statement is true about the dilation?

arsen [322]

Answer:

Option (B) is true i.e segment B'D' will run through (2,2) and will be longer than the segment BD.

Step-by-step explanation:

As the assumption quadrilateral ABCD is shown in figure a.

First located the center of the dilation which is located at (2,2) as shown in figure b.

The next thing we want to do is to determine the distance of the center of dilation to each of the points of quadrilateral ABCD as shown in figure b.

Let’s just start with the distance from the center to the point A, but notice we don’t have to move up and down in y direction. So, what we have to do is to increase this by the factor 2. Because this horizontal distance is 1 i.e. the distance from dilation center (2,2) to point A, we just have to multiply by 2 which would be a distance of 2 and this point right here will be the new location of point A’ (0,2).

And the distance from the center to the point C is the horizontal distance of 2 i.e. the distance from dilation center (2,2) to point C, we just have to multiply by 2 which would be a distance of 4 and this point right here will be the new location of point C’ (6,2).

And the distance from the center to the point B is the upward vertical distance of 1 i.e. the distance from dilation center (2,2) to point B, we just have to multiply by 2 which would be a vertical distance of 2 and this point right here will be the location of point B’ (2,4).

And similarly the distance from the center to the point D is the downward vertical distance of 1 i.e. the distance from dilation center (2,2) to point D, we just have to multiply by 2 which would be a vertical distance of 2 and this point right here will be the location of point D’ (2,0).

So, Quadrilateral A'B'C'D' is dilated by a scale factor of 2 centered around (2, 2).

Just notice in figure b that the segment B'D' will run through (2,2) and will be longer than the segment BD.

So,option (B) is true i.e segment B'D' will run through (2,2) and will be longer than the segment BD.

Learn more about dilation from brainly.com/question/12528454

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