Graph the image of this figure after a dilation with a scale factor of centered at the origin.

Mathematics

1 answer:

kvv77 [185]1 year ago

7 0

A picture of the dilated figure with its points at (-2, 10), (2, 6), and (-8, 4) is provided.

<h3 /><h3>What exactly is dilation?</h3>

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

The complete question is;

"Graph the image of this figure after a dilation with a scale factor of 2 centered at (2, 2) .

Use the polygon tool to graph the dilated figure."

The center of dilation and figure are first translated, making the origin the center of dilation.

We map every point because the point (2, 2), which is our center of dilatation, must be translated left 2 and down 2 to become the origin.

(x, y)→(x-2, y-2)

Each point will be multiplied by two when the scale factor is two, giving us the rule.

(x, y)→(2x-4, 2y-4)

In order to return the figure to its original location, we must translate it right 2 and up 2; this gives us the rule.

(x,y)→(2x-4+2, 2y-4+2) = (2x-2, 2y-2)

At the top of the original figure, the first point is (0, 6). When we use the transformation, we get

(0, 6)→(2*0-2, 2*6-2) = (0-2, 12-2) = (-2, 10)

The pre-rightmost image's point is (2, 4). The results of using the transformation rule are;

(2, 4)→(2*2-2, 2*4-2) = (4-2, 8-2) = (2, 6)

The pre-leftmost image's point is at (-3, 3). The transformation rule being applied, w

(-3, 3)→(-3*2-2, 3*2-2) = (-6-2, 6-2) = (-8, 4)

Hence,an picture of the dilated figure with its points at (-2, 10), (2, 6), and (-8, 4) is provided.