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A transformation determined by a center point and a scale factor is known as a dilation. In this transformation, all points in a geometric figure are moved away from or toward the center point by a factor of the scale. If the scale factor is greater than 1, the figure enlarges; if it is between 0 and 1, the figure shrinks. This transformation preserves the shape of the figure but alters its size.
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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.
A transformation in which the figure grows larger is called?
A transformation in which the figure grows larger is called dilation. In dilation, every point of the figure is moved away from a fixed center point by a scale factor greater than one. This results in a proportional increase in the size of the figure while maintaining its shape.
What is a transformation that turns a figure around a given point?
A transformation that turns a figure around a given point is called a rotation. In a rotation, every point of the figure moves in a circular path around the center point, known as the center of rotation, by a specified angle. The distance from each point to the center remains constant, and the orientation of the figure changes according to the direction and degree of rotation. This transformation preserves the shape and size of the figure.
Which type of transformation turns a figure around a fixed point?
A rotation is the type of transformation that turns a figure around a fixed point, known as the center of rotation. During a rotation, every point of the figure moves in a circular path around this fixed point by a specified angle. The distance from the center to any point on the figure remains constant throughout the transformation.
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) ).
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.
Is a transformation that turns a figure to a fixed point?
An enlargement with a scale factor of 0.
A transformation in which the figure grows larger is called?
A transformation in which the figure grows larger is called dilation. In dilation, every point of the figure is moved away from a fixed center point by a scale factor greater than one. This results in a proportional increase in the size of the figure while maintaining its shape.
What transformation is equivalent to reflection over a point geometry?
Reflection over a point is equivalent to enlargement with the same point as the focus of enlargement and a scale factor of -1.
What is the name of the transformation in which each point on a figure is turned through a given angle and direction around a given point?
The transformation you're referring to is called rotation. In a rotation, each point of a figure is turned around a specific point, known as the center of rotation, through a specified angle and direction (clockwise or counterclockwise). This transformation preserves the shape and size of the figure while changing its orientation.
What is a polar inversion?
A polar inversion is a geometric transformation that swaps each point through a circle with its antipodal point. It is also known as a circle inversion, where the center of inversion is the center of the circle, and points inside the circle are mapped outside while points outside are mapped inside. This transformation preserves angles but distorts distances.
What is the number of decimal places in the factor 40?
The number of decimal places in a factor is determined by counting the digits to the right of the decimal point. In the case of the factor 40, there are no decimal places, as there is no decimal point present. Therefore, the number of decimal places in the factor 40 is 0.
What is true transformation efficiency?
True transformation efficiency is the transformation efficiency at the saturation point, or essentially the highest transformation efficiency that can be attained.
How does dilation effect the coordinates of dilated points?
Well this is my thought depending on where the point of dilation is the coordinates of the give plane is determined. The point of dilation not only is main factor that positions the coordinates, but the scale factor has a huge impact on the placement of the coordinates.
What is the image of P for a dilation with center (0 0) and a scale factor of 2.5 p is (1-2)?
Multiply the distance of each coordinate from the center by the scale factor to get the new position: new_coord = center_coord + (old_coord - center_coord) x scale_factor. The x and y coordinates are worked out separately; for (1, -2), center (0, 0), scale factor 2.5: new_x = 0 + (1 - 0) x 2.5 = 2.5 new_y = 0 + (-2 - 0) x 2.5 = -5 → P (1, -2) goes to (2.5, -5) under the transformation.
What does dialation mean in math context?
In mathematics, dilation refers to a transformation that alters the size of a geometric figure while maintaining its shape and proportions. This involves resizing the figure by a scale factor relative to a fixed point known as the center of dilation. A scale factor greater than one enlarges the figure, while a scale factor between zero and one reduces it. Dilation is commonly used in geometry to study similar figures and their properties.
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).
