How can dilation scale factors help you identify points on a line passing through the origin given one additional point?.

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19-12-2022
Mathematics

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How can dilation scale factors help you identify points on a line passing through the origin given one additional point?.

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smecloudbird18 smecloudbird18 · Answer 1 · 2022-12-22T01:32:37-05:00

Dilation scale factors can help you identify points on a line passing through the origin given one additional point by forming right triangle with the vertices at the origin, the additional Point P, and a leg along the x-axis.

Therefore the answer is d) The scale factor can be used by forming a right triangle with vertices at the origin, the additional Point P, and a leg along the x-axis. Any dilation applied to this triangle will plot a new point on the line, the image of P.

Dilation is the process of increasing or decreasing an object's size without altering its shape. Depending on the scale factor, the object's size may increase or shrink.

Scale factor is the ratio of dimension of the new shape to the dimension of the original shape. A shape factor greater than 1 implies the object enlarges, less than 1 means the object contracts and equal to 1 means the shape remains the same.

The centre of dilation is where the resizing begins. The objects or figures are enlarged or shrunk from the centre of dilatation.

The scaling factor can be applied by forming a right triangle with vertices directly at the origin, Point P as an additional point, and a leg down the x-axis. As a result, this triangle will draw a new point on the line that is the image of P with any dilation applied.

-- The question is incomplete, the correct question is as follows --

"How can dilation scale factors help you identify points on a line passing through the origin given one additional point? a) The line passing through the origin can be the hypotenuse of the legs of triangles that are similar. b) The dilation scale factor can be used to determine the side lengths of the legs but not the hypotenuse of similar triangles. c) All triangles produced through dilation are similar, so the points will be on the same line. d) The scale factor can be used by forming a right triangle with vertices at the origin, the additional Point P, and a leg along the x-axis. Any dilation applied to this triangle will plot a new point on the line, the image of P."

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