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What is A transformation that is determined by a center point and a scale factor?
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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 definition in math terms of transformation?
Transformation in maths is when you shift a point or multiple points in terms of it's original point. Ie if you were to shift the point (2;1) about the x axis the transformed point would be (-2;1).
What type of transformation turns a figure about a point?
A rotation
What is a transformation in which you turn a figure about a fixed point?
a pivot
A transformation that proportionally reduces or enlarges a figure?
Scaling will proportionally reduce or enlarge a figure. The amount of scaling is given by the scale factor (greater than zero) If the scale factor is less than 1, the figure is reduced and it is sometimes called a contraction If the scale factor is greater than 1, the figure is enlarged, and it is called a dilation or enlargement. If a centre of enlargement is used, the distance of every point from the centre is multiplied by the scale factor. The scale factor can be negative in which case the distance to the new point is measured on the opposite side of the centre to the original point.
Is a transformation that turns a figure to a fixed point?
An enlargement with a scale factor of 0.
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 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 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 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 definition in math terms of transformation?
Transformation in maths is when you shift a point or multiple points in terms of it's original point. Ie if you were to shift the point (2;1) about the x axis the transformed point would be (-2;1).
What is the rule for the transformation above?
The rule for the transformation above is translation. Translation is a transformation that moves every point of a figure the same distance in the same direction.
Is it true that a circle is determined if a given segment is its diameter?
Yes. The center is the mid-point of the segment, and that's all you need to uniquely define a circle.
How is the center of the gravity determined when an object is at rest or in motion?
The center of gravity of an object at rest can be determined by locating the point where the weight is evenly distributed in all directions. For objects in motion, the center of gravity can shift depending on the position and orientation of the object. Calculations or measurements of mass distribution are typically needed to determine the center of gravity accurately.
What is the definition for a transformation in which a figure is turned about a point?
rotation
