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What does the line of symmetry do?
It indicates a line such that a shape can be reflected over than line such that the image is similar to the original.
What is the shortest distance between a point and a line?
The length of a line segment that starts at the point and is perpendicular to the original line.
What is a line that a figure is flipped across to create a mirror imge of the original figure?
It is a line of symmetry
What is the shortest distance between a straight line and a curve?
If you translate (move without rotation) a copy of the line towards the curve, the first point where the line touches the curve (the tangent to the curve with the slope of the original line) will be the point on the curve closest to the line. Draw a connecting line from this tangent point to the original line, intersecting that original line at right angles. Measure the connecting segment. It is the shortest distance. Vector analysis will give a mathematically strict solution, I do not have the ability to explain this in sufficient detail.
You draw a line without touching it how do you make the line longer?
To make a line longer without touching it, you can create the illusion of length by drawing additional lines parallel to the original line, extending outward from its ends. Alternatively, you could simply draw another line that connects to the original line's endpoints, effectively increasing its perceived length.
