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September 12, 2023

Which Graph Shows a Dilation?

A dilation is a transformation that makes a figure larger or smaller by a specified scale factor. The new figure is called the image and the original is called the pre-image.

A cervix check can give your doctor an idea of how dilated you are and when labor might start. Doctors and midwives often check the cervix manually by wearing sterile gloves and putting two fingers in the vaginal canal to feel for cervical effacement and cervical dilation. You're considered 1 centimeter dilated if you can fit one finger into your cervix. A second finger can tell your doctor that you're 2 centimeters dilated. Some doctors will also use an internal exam with an ultrasound to get a more precise measurement of your cervix.

There are three kinds of isometric transformations of a graph: translations, rotations and reflections. A dilation is a non-isometric transformation that changes the size of a figure while preserving its shape.

Let's consider the triangle ABCABC below. A dilation is a transformation that makes this triangle bigger or smaller by an exact value (or to be more precise, a linear function of x). Suppose we want to find which graph shows a dilation. We can either slide the triangle kk units to the left and 22 units up or dilate it by ekek from the yy-axis. Both of these graphs have the same shape, but the dilated triangle is larger than the original one. The equation of the transformed triangle is the ratio between the geometric distances of its vertices and the shortest path distances.