Figure Dilation
Figure Dilation - Related Videos
03:34
Uncertainty in Measurement: Significant Figures
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2020
All the digits in a measurement, including the uncertain last digit, are called significant figures or significant digits. Note that zero may be a measured value; for example, if a scale that shows weight to the nearest pound reads “140,” then the 1 (hundreds), 4 (tens), and 0 (ones) are all significant (measured) values. A measurement result is properly reported when its significant digits accurately represent the certainty of the measurement process. Below are a set of rules to determine the...
07:45
Quantifying Intermembrane Distances with Serial Image Dilations
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Cited by 11 •
2018
The purpose of this algorithm is to continuously measure the distance between two 2-dimensional edges using serial image dilations and pathfinding. This algorithm can be applied to a variety of fields such as cardiac structural biology, vascular biology, and civil engineering.
01:44
Rules for Significant Figures
0 Views •
2023
In any measurement, the precision of the measuring tool is an essential factor. An ordinary ruler, for example, can measure length to the closest millimeter; a caliper, on the other hand, can measure length to the nearest 0.01 mm. As a result, the caliper is a more precise measurement tool because it can measure extremely minute changes in length. The measurements will be more accurate if the measuring tool is more precise. It should be emphasized that when we represent measured values, the...
01:44
Rules of Significant Figures
0 Views •
2023
In any measurement, the precision of the measuring tool is an essential factor. An ordinary ruler, for example, can measure length to the closest millimeter; a caliper, on the other hand, can measure length to the nearest 0.01 mm. As a result, the caliper is a more precise measurement tool because it can measure extremely minute changes in length. The measurements will be more accurate if the measuring tool is more precise. It should be emphasized that when we represent measured values, the...
00:58
Significant Figures in Calculations
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2023
Uncertainty in measurements can be avoided by reporting the results of a calculation with the correct number of significant figures. This can be determined by the following rules for rounding numbers: When adding or subtracting numbers, round the result to the same number of decimal places as the number with the least number of decimal places. When multiplying or dividing numbers, round the result to the same number of digits as the number with the least number of significant figures. If...
FAQs
The center of dilation provides the reference point for every movement. A point and its image lie on the same line through that center, while the scale factor determines how far the image lies from it. This shared alignment makes the transformation systematic and helps identify corresponding points when constructing or checking a dilated figure.
The scale factor multiplies each point’s distance from the center by the same amount. A factor greater than one places image points farther away, whereas a factor between zero and one places them closer. Because the same multiplier applies throughout the figure, proportional relationships are preserved while the overall size changes.
When the center of dilation is the origin, the rule (x, y) maps to (kx, ky). Applying this rule separately to each coordinate gives the image of every vertex without measuring distances by hand. It also makes the scale factor visible in the coordinates, supporting precise calculations and comparisons between the original and image.
First, identify the scale factor and confirm that the center is the origin if using the rule (x, y) to (kx, ky). Then multiply both coordinates of each vertex by that factor and plot the resulting points. Connecting the image vertices in their original order produces the transformed figure for inspection or further calculation.
A scale drawing represents measurements by applying a common scale factor to the original figure. Lengths in the drawing therefore maintain the same proportional relationships as the corresponding lengths in the original. This allows a researcher or student to use a known measurement and the scale factor to determine an associated image measurement.
The comparison can focus on corresponding positions, distances from the center, angle measures, and proportional size. Each image point should lie on the appropriate line through the center, and its distance should match the original distance multiplied by the scale factor. These checks help verify whether a plotted image represents the intended transformation.
Figure dilation supports similarity, scale drawings, proportional reasoning, and geometric modeling. In these settings, the transformation connects an original figure with a larger or smaller representation while retaining its shape and angle measures. Coordinate rules provide an efficient computational model, while the center and scale factor explain the geometric relationship between the two figures.