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3 years ago

A dilation centered at the origin is applied to the line y = 3x + 5.

Mathematics

2 answers:

SOVA2 [1]3 years ago

8 0

Answer:

"The question cannot be answered without knowing the scale factor."

Step-by-step explanation:

The complete question:

A dilation centered at the origin is applied to the line y = 3x + 5. What is true about the image of the line?

It is the same line.
It is another line parallel to y = 3x + 5.
The image is not a line.
The question cannot be answered without knowing the scale factor.

A dilation, center at origin, with a scale factor of "k", will have a rule:

(x,y) = (kx,ky)

This basically means that the image after dilation will have the points kx and ky respectively.

If k ≠ 1, this means the image is parallel to the line y = 3x + 5

If k = 1, this means the image is same, it coincides with the line y = 3x + 5

Thus, the scale factor is really important and we can't say anything about this dilation since scale factor isn't known.

Natalija [7]3 years ago

7 0

Answer:

"The question cannot be answered without knowing the scale factor."

Step-by-step explanation:

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Select all the statements that are true

masya89 [10]

Answer:

Options 2, 4 and 6 are True.

Step-by-step explanation:

Triangle MNO is dilated by a scale factor of $\frac{3}{2}$ centered at M(0, 6).

Rule to be followed to dilate the vertices of the given triangle,

(x, y) → (kx, ky)

Here, k = scale factor

By this rule vertices of the new triangle M'N'O' will be,

M(0, 6) → M'(0, 6) [Coordinates of M' will remain same as M because center of dilation is point M]

N(-4, -4) → N'(-6, -6)

O(6, -2) → O'(9, -3)

Option 1

M'N' is shorter than MN

Distance between M and N = $\sqrt{(0+4)^2+(6+4)^2}$

= 10.77

Distance between M' and N' = $\sqrt{(0+6)^2+(6+6)^2}$

= 13.42

Therefore M'N' > MN

Therefore, Option A is False.

Option 2

ON is shorter than O'N'

True.

Option 3

OM is longer than O'M'

False

Option 4

ON is parallel to O'N'

Since OM and MN are dilated with the same scale factor, O'N' will be parallel to ON.

True.

Option 5

OM is parallel than O'M'

Since, O'M' is the dilated form of OM,

Therefore, all the points (O, M and M') will be in a straight line.

False

Option 6

M'N' coincide with MN

True.

Therefore, Options 2, 4 and 6 are True.

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