The dilation (image) must lie on that line, which it does. You can check this by drawing a line from the center of dilation through the preimage point. Multiplying these distances times the scale factor, 4, means our new point must be 12 horizontal (x-axis) units from the center of dilation, and 8 vertical (y-axis) units from the same center of dilation, at (13, 11). The plotted point of our preimage is 3 horizontal units away from the center of dilation. You are essentially calculating the slope of the line from the center of dilation to both coordinate pairs (preimage and image): Calculating slope from center of dilation You are asked to plot the image point using a scale factor of 4. Here is a point (4, 5) with the center of dilation at (1, 3). The "distance" from the center of the dilation to each point is calculated as the difference between the two sets of coordinate points. You can move the center to any place on the coordinate plane you wish. The trapezoid used our origin (0, 0) as the center of dilation. Notice that the vertices of our image points share almost the same designation as the preimage vertices, but with the prime indicator: A', B', C', D'. The two polygons are similar: Dilation on the coordinate plane example The new dilation is also the same shape as the preimage. The image or enlargement has sides twice the length of the original preimage trapezoid. Dilation does not change the shape of the object from preimage to image, only its position.
Dilation is one of the five major transformations in geometry. Point C at (3, -1) enlarges to C' at (6, -2) Examples Dilation definition Dilation is the enlarging or shrinking of a mathematical element (a point on a coordinate grid, polygon, line segment) using a specific scale factor. Point B at (1, 1) enlarges to B' at (2, 2) Vertex D in the preimage at (-3, -1) becomes D' at (-6, -2) for the image.Ĭan you calculate the coordinates for vertices B' and C'? Take the coordinates of vertex A in the preimage at (-2, 1) and multiply times 2, producing (-4, 2) as the new A' for the image.
Here is a trapezoid on a coordinate grid with the origin (0, 0) as the center of dilation: Trapezoid with origin as center of dilationį we choose a scale factor of 2, every plotted point on the polygon will be multiplied by 2 to create the enlarged image. Let's see the scale factor at work on a coordinate plane. Scale factor of dilation Dilation examples If you multiply the original coordinates:īy whole numbers other than 1, you enlarge the preimage in producing the image.īy 1, you produce an image congruent to the preimage.īy fractions or decimals, you shrink the preimage to produce the image.īy negative numbers, you will produce an image that is the inverse (upside down) of the preimage, equidistant from the center of dilation but on the opposite side.
The scale factor of a dilation is the amount by which all original terms are enlarged or shrunk, usually on a coordinate plane. Here we still have a square as the preimage, but the center of the dilation is the top-left vertex, so the dilated images (one smaller, one larger) all share that same vertex. The center of the dilation does not need to be inside the shape. Its center of dilation is its exact middle, so any dilation from the square will still be a square with all parts equidistant from the center point: Center of dilation pre-image and image You can think of the preimage as the original figure, and the image as the new figure. The preimage and image are similar figures. Dilation - math definitionįrom that center of dilation, the preimage – the mathematical element before scaling – is enlarged, inverted, or shrunk to form the image.
This can be a single point on a coordinate grid, the middle of a polygon, or any fixed point in space. If V W ‾ ≅ X Y ‾ \overline J K ∥ N O start overline, J, K, end overline, \parallel, start overline, N, O, end overline.
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