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3 years ago

Plot the image of point D under a dilation about the origin (0,0) with a scale factor of 3.

Mathematics

1 answer:

babunello [35]3 years ago

3 0

Answer:

D'(-6, 0) is the image of point D(-2, 0) under a dilation about the origin (0,0) with a scale factor of 3, as shown in attache figure below.

Please check the attache graph below where you can check the plot of the image D' of point D.

Step-by-step explanation:

As the point D on the coordinate plane has the vertex location

D(-2, 0)

The rule of dilation about the origin (0,0) with a scale factor of 3:

The rule states that if we dilate the point, let say D(-2, 0), under a dilation about the origin (0,0) with a scale factor of 3, all we need to multiple the coordinates of the point D with 3. The result will be the image of point D.

P(x, y) → P'(3x, 3y)

D(-2, 0) → D'(-6, 0) ∵ (-2×3, 0×3)=(-6, 0)

Therefore, the image of point D under a dilation about the origin (0,0) with a scale factor of 3 can be plotted at the location D'(-6, 0).

So the new location of D' is (-6, 0).

D'(-6, 0) is the image of point D(-2, 0) under a dilation about the origin (0,0) with a scale factor of 3, as shown in attache figure below.

Please check the attache graph below where you can check the plot of the image D' of point D.

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Where do I place the coordinates for -2x-5 and -x-4

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Step-by-step explanation:

you need to calculate coordinates first. just by having the function definitions you don't have any coordinates yet.

I typically pick x = 0 as a first point.

so, that gives

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as y result for the first line.

the point on line 1 is then (0, -5)

and we get -0 - 4 = -4 as y result for the second line.

the point for the second line is (0, -4)

for second points I typically go for x = 1.

for the first line we get

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and the second point is (1, -7) for the first line.

for the second line we get

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and the second point is (1, -5) for the second line.

so, make points on the chart for all 4 points, and connect them (and extend the connecting lines to the left and right to the end of the grid).

and the crossing point ?

that is where both equations deliver the same result.

so,

-2x - 5 = -x - 4

-x = 1

x = -1

and the y is then e.g. -2×-1 - 5 = 2 - 5 = -3

and the crossing point is (-1, -3)

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