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2 years ago

WILL GIVE BRAINLIEST

Mathematics

1 answer:

EastWind [94]2 years ago

7 0

Answer:

Let coordinates of vertex D be (x,y)

In parallelogram diagonals are bisect each other.

∴ Mid-point of AC= Mid-point of BD

⇒ (

3+(−6)

−4+2

)=(

−1+x

−3+y

)

⇒ (

−3

−2

)=(

−1+x

−3+y

)

⇒ (

−3

,−1)=(

−1+x

−3+y

)

Now,

⇒

−3

−1+x

⇒ −6=−2+2x

⇒ −4=2x

∴ x=−2

⇒ −1=

−3+y

⇒ −2=−3+y

⇒ 1=y

∴ y=1

∴ Coordinates of vertex D is (−2,1)

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These are the transformations of interest:

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g(x) = f(x) +k . . . . vertical translation by k units (upward)

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The vertical and horizontal transformations can be applied in either order, since neither affects the other. If we work left-to-right through the expression for g(x), we can see these transformations have been applied:

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reflection over the y-axis . . . 1/3f(-x)
horizontal scaling by a factor of 3 (expansion) . . . 1/3f(-1/3x)
translation left 1 unit . . . 1/3f(-1/3(x+1))
translation up 3 units . . . 1/3f(-1/3(x+1)) +3

_____

<em>Additional comment</em>

The "working" is a matter of matching the form of g(x) to the forms of the different transformations. It is a pattern-matching problem.

The horizontal transformations could also be described as ...

translation right 1/3 unit . . . f(x -1/3)
reflection over y and expansion by a factor of 3 . . . f(-1/3x -1/3)

The initial translation in this scenario would be reflected to a translation left 1/3 unit, then the horizontal expansion would turn that into a translation left 1 unit, as described above. Order matters.

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