if a scale factor of four is used, the points in the image will be eight times as far from the origin as at he pre-image points true or false
where does the 4-times scaling take (x,y) --> ?
Is it 8 times as far from the origin or not?
I would say false
To determine whether the points in the image will be eight times as far from the origin as the pre-image points when a scale factor of four is used, we need to understand how scaling works.
When an object or set of points is scaled up or down by a scale factor, the distance between points and the origin (or any reference point) changes proportionally. In this case, if the scale factor is four, it means that the image will be four times larger than the pre-image in all dimensions.
To find out how the distance from the origin changes, we can use the formula:
Distance to image = Scale factor × Distance to pre-image
So, let's calculate the change in distance using the scale factor of four:
Distance to image = 4 × Distance to pre-image
Now, if the scale factor is four, the distance to the image will be four times the distance to the pre-image. Therefore, the statement "the points in the image will be eight times as far from the origin as at the pre-image points" is false. The correct statement would be that the points in the image will be four times as far from the origin as at the pre-image points.