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Kamila [148]
3 years ago
5

Given a dilation with the origin O (0, 0), by observation determine the scale factor "K."

Mathematics
2 answers:
nirvana33 [79]3 years ago
5 0

Answer:

The correct option is 1. The scale factor is 1/2.

Step-by-step explanation:

The given rule of dilation is

D_{o,K}:(6,12)\rightarrow (3,6)

Where, o is origin or center of dilation and K is scale factor.

If a figure is dilation by scale factor K and center of dilation at origin, then

P(x,y)\rightarrow P'(kx,ky)

It means

\text{Scale Factor}=\frac{\text{x-coordinate of image}}{\text{x-coordinate of preimage}}

K=\frac{3}{6}

K=\frac{1}{2}

The scale factor is 1/2. Therefore the correct option is 1.

BaLLatris [955]3 years ago
4 0
When the dilation is about the origin, the scale factor multiplies every coordinate. That is (considering the x-coordinate) ...
  6·k = 3
  k = 3/6 = 1/2

The appropriate choice is
  1. 1/2
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Line DE contains the points D (–1, –4) and E (3, 3). Line FG contains the point F (–3, 3). Which set of coordinates for point G
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Answer:

The set of coordinates for point G that make the two lines perpendicular are given through the relation

7y = -4x + 9

Step-by-step explanation:

The condition for perpendicularly of two lines is that the products of the slope of the two lines, m₁ and m₂ must be equal to -1.

For a line whose two points (x₁, y₁) and (x₂, y₂)

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Let the slope of DE be m₁ and the slope of FG be m₂

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m₁m₂ = -1

m₁ = (Δy/Δx) = (-4 - 3) ÷ (-1 -3) = (7/4) = 1.75

Since, m₁m₂ = -1, this means that,

m₂ = (-1/m₁) = (-1/1.75) = -(4/7)

Let the coordinates of point G be (x, y)

m₂ = (3 - y) ÷ (-3 - x)

(-4/7) = [(3-y)/(-3-x)]

-4(-3-x) = 7(3-y)

12 + 4x = 21 - 7y

7y = -4x + 9

Hope this Helps!!!

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