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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 C(9 3) when dilated with a scale factor of ⅓ using the point (3 6) as the center of dilation?
To find the transformation of the point C(9, 3) when dilated with a scale factor of ⅓ from the center of dilation (3, 6), you first subtract the center coordinates from C's coordinates: (9 - 3, 3 - 6) = (6, -3). Then multiply by the scale factor of ⅓: (6 * ⅓, -3 * ⅓) = (2, -1). Finally, add the center coordinates back: (2 + 3, -1 + 6) = (5, 5). Thus, the transformed point is (5, 5).
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 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 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 point of transformation does not move in isometry?
In an isometry, the point of transformation that does not move is called the "fixed point." This point remains unchanged during the transformation, whether it is a translation, rotation, or reflection. For example, in a rotation, the center of rotation serves as the fixed point, while in a reflection, the line of reflection equidistantly bisects the space, with points on the line remaining unchanged.
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 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.
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.
