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To find the scale factor of a dilation with the center at the origin, you can compare the coordinates of a point before and after the dilation. If a point ( P(x, y) ) is dilated to ( P'(x', y') ), the scale factor ( k ) can be calculated using the formula ( k = \frac{x'}{x} = \frac{y'}{y} ), assuming ( x ) and ( y ) are not zero. This scale factor indicates how much the original point has been enlarged or reduced.
What else can I help you with?
What are the coordinates of the image of the point (-412) under a dilation with a scale factor of 4 and the center of dilation at the origin?
If the original point was (-4, 12) then the image is (-16, 48).
What is the transformation of B(4 8) when dilated by a scale factor of 2 using the origin as the center of dilation?
To find the transformation of point B(4, 8) when dilated by a scale factor of 2 using the origin as the center of dilation, you multiply each coordinate by the scale factor. Thus, the new coordinates will be B'(4 * 2, 8 * 2), which simplifies to B'(8, 16). Therefore, point B(4, 8) transforms to B'(8, 16) after the dilation.
How do you find coordinate's dilated?
To find the coordinates of a point after dilation, you multiply the original coordinates by the scale factor. If the point is represented as ( (x, y) ) and the scale factor is ( k ), the new coordinates become ( (kx, ky) ). If the dilation is from a center point other than the origin, you would first subtract the center coordinates from the point, apply the scale factor, and then add the center coordinates back to the result.
What is the transformation of c(93) when dilated by a scale factor of 3 using the origin as the center of dilation?
To dilate the point ( c(93) ) by a scale factor of 3 using the origin as the center of dilation, you multiply the coordinates of the point by 3. If ( c(93) ) refers to the point ( (9, 3) ), the transformed coordinates would be ( (9 \times 3, 3 \times 3) = (27, 9) ). Therefore, the transformed point after the dilation is ( c(27, 9) ).
How do you enlarge a figure on a coordinate graph?
To enlarge a figure on a coordinate graph, you can apply a dilation transformation using a scale factor. Choose a center point for the dilation, often the origin or the center of the figure, and multiply the coordinates of each vertex by the scale factor. For example, if you use a scale factor of 2, each coordinate (x, y) becomes (2x, 2y), effectively doubling the size of the figure while maintaining its shape and proportions.
Triangle ABC below will be dilated with the origin as the center of dilation and scale factor of 1/2?
0.5
Every dilation has a?
Center and Scale Factor....
What is the transformation of C(9 3) when dilated by a scale factor of 3 using the origin as the center of dilation?
It is (27, 9).
What are the coordinates of the image of the point (-412) under a dilation with a scale factor of 4 and the center of dilation at the origin?
If the original point was (-4, 12) then the image is (-16, 48).
What is the transformation of B(4 8) when dilated by a scale factor of 2 using the origin as the center of dilation?
To find the transformation of point B(4, 8) when dilated by a scale factor of 2 using the origin as the center of dilation, you multiply each coordinate by the scale factor. Thus, the new coordinates will be B'(4 * 2, 8 * 2), which simplifies to B'(8, 16). Therefore, point B(4, 8) transforms to B'(8, 16) after the dilation.
How do you find coordinate's dilated?
To find the coordinates of a point after dilation, you multiply the original coordinates by the scale factor. If the point is represented as ( (x, y) ) and the scale factor is ( k ), the new coordinates become ( (kx, ky) ). If the dilation is from a center point other than the origin, you would first subtract the center coordinates from the point, apply the scale factor, and then add the center coordinates back to the result.
What are the two key characteristics of a dilation?
The two key characteristics of a dilation are the center of dilation and the scale factor. The center of dilation is a fixed point in the plane from which all other points are expanded or contracted. The scale factor determines how much the figure is enlarged or reduced; a scale factor greater than one enlarges the figure, while a scale factor between zero and one reduces it. Dilation preserves the shape of the figure but changes its size.
How do you solve dilation?
To solve a dilation problem, you first need to identify the center of dilation and the scale factor. The scale factor indicates how much larger or smaller the figure will be compared to the original. For each point on the original figure, you calculate the new coordinates by multiplying the distances from the center of dilation by the scale factor. Finally, plot the new points to create the dilated figure.
What is the transformation of c(93) when dilated by a scale factor of 3 using the origin as the center of dilation?
To dilate the point ( c(93) ) by a scale factor of 3 using the origin as the center of dilation, you multiply the coordinates of the point by 3. If ( c(93) ) refers to the point ( (9, 3) ), the transformed coordinates would be ( (9 \times 3, 3 \times 3) = (27, 9) ). Therefore, the transformed point after the dilation is ( c(27, 9) ).
How do you enlarge a figure on a coordinate graph?
To enlarge a figure on a coordinate graph, you can apply a dilation transformation using a scale factor. Choose a center point for the dilation, often the origin or the center of the figure, and multiply the coordinates of each vertex by the scale factor. For example, if you use a scale factor of 2, each coordinate (x, y) becomes (2x, 2y), effectively doubling the size of the figure while maintaining its shape and proportions.
How do you graph a dilation?
To graph a dilation, first identify the center of dilation and the scale factor. For each point of the original figure, measure the distance from that point to the center of dilation, then multiply that distance by the scale factor to find the new distance from the center. Plot the new points at these distances, and connect them to form the dilated figure. Ensure that the orientation remains the same and that the shape is proportional to the original.
A photographer knows that the center of a camera lens acts as a center of dilation, where the image of an object forms behind the lens.Is the scale factor for this dilation negative or positive?
Negative
