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How do you dialate a shape by 3?
To dilate a shape by a factor of 3, multiply the coordinates of each vertex of the shape by 3. For example, if a vertex is at (x, y), after dilation it will be at (3x, 3y). This process enlarges the shape while maintaining its proportions and the center of dilation, which is typically the origin (0,0) unless specified otherwise.
Does dilation change the shape?
Geometric dilation (size change, typically expansion) does not change the shape of a figure, or its center location, only the size.
What happens if you enlarge a shape by a negative scale factor but multiply each of the original distances from vertex to centre by your negative scale factor?
If you enlarge a shape by a negative scale factor, the shape not only changes size but also reflects across the center point (the origin). Multiplying each original distance from a vertex to the center by a negative scale factor effectively inverts the position of each vertex relative to the center, resulting in a shape that is both enlarged and flipped. This transformation can lead to a shape that occupies a different quadrant or orientation in the coordinate system.
What does k mean in dilation?
In dilation, "k" refers to the scale factor that determines how much a shape is enlarged or reduced. If k is greater than 1, the shape is enlarged; if k is between 0 and 1, the shape is reduced. The dilation is centered at a specific point, often called the center of dilation, which affects the positioning of the transformed shape. Thus, "k" directly influences the size and proportion of the original figure.
How do you dilate a shape in math?
To dilate a shape in math, you need a center of dilation and a scale factor. The center of dilation is a fixed point from which all other points of the shape will move. The scale factor determines how much the shape enlarges or shrinks; for example, a scale factor greater than 1 enlarges the shape, while a factor between 0 and 1 reduces it. To find the coordinates of the dilated shape, multiply the distance of each point from the center by the scale factor and then apply that to the center's coordinates.
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.
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.
Why does a dilation transform a figure?
A dilation transforms a figure by scaling it proportionally from a fixed center point, known as the center of dilation. This process changes the size of the figure while maintaining its shape and the relative positions of its points. Each point in the original figure moves away from or toward the center of dilation based on a specified scale factor, resulting in a larger or smaller version of the original figure. Thus, dilation preserves the geometric properties, such as angles and ratios of distances.
Not a shape it has one vertex angle of the vertex is 90 degrees what shape is it?
L shape
What shape has no vertex?
A circle does not have a vertex.
What happens when you dilate a triangle with a scale factor of 2?
When you dilate a triangle with a scale factor of 2, each vertex of the triangle moves away from the center of dilation, doubling the distance from that point. As a result, the new triangle retains the same shape and angles as the original triangle but has sides that are twice as long. This means the area of the dilated triangle becomes four times larger than the original triangle's area.
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.
