If you're taking a geometry course in middle or high school, you will likely need to learn how to reflect points and shapes across lines. This is an extension to beginner reflections (basically drawing a shape on a piece of paper and folding it in half to understand what reflections are) that you may have done in elementary school. This article will show you how to reflect a shape over a line using a protractor and a straightedge.
Steps
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Place your protractor on a point of your shape. Place the center of your protractor on the point you've selected. There is usually a hole or a vertical line that marks the middle of a protractor. Place the hole or line on the first point of your shape. You can either reflect the points in alphabetical order, or reflect the point closest to the line of reflection.
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Line up the protractor with your line of reflection. The horizontal part of your protractor and your line of reflection need to form a right angle, which is an angle that measures 90 degrees. This means that your line of reflection should touch the "90" on your protractor. If it doesn't, line it up or straighten your protractor more. [1] X Research source
- Don't completely move it, as your protractor still needs to touch the point that you are reflecting.
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Draw a line using the straight part of your protractor. When your line of reflection is at the 90-degree tick mark on your protractor, mark a perpendicular line using a straightedge or the straight part of your protractor. Making it longer is often beneficial, as your point may be further away from your line of reflection, making your reflected point equidistant (the same distance) from the line as well.
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Measure the distance from your original point and the line of reflection. If your perpendicular line extends further than the distance of your point and the line of reflection, erase part of it. For example, if the distance from A and line x is 5 centimeters and you find that your perpendicular line on the reflected side of your line is 8 centimeters, erase 3 centimeters of your line to make 5 centimeters. [2] X Research source
- This is because the original point (the preimage) and the reflected point (the image) have to be the same distance from the line of reflection.
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Mark your point. After you've made sure that your line has equal distance on both sides of the line of reflection, mark your point. Mark it (name of point)'. The apostrophe represents a similar yet distinct image. You'll use the apostrophe not only in grammar (in contractions and possessives) but also in geometry. You'll use this symbol to represent shapes that have been reflected, translated, rotated, or dilated.
- For example, if your point is point N and you've reflected it over line A, mark your reflected point N'.
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Things You'll Need
- Protractor
- Ruler
- Pencil
- Piece of paper (preferably white paper and not graph paper)
Tips
- Try not to move your paper or change your compass setting while reflecting your shape. You may draw your figure inaccurately if this happens.Thanks
- If you're practicing reflections, do not draw your shape on the grid lines of graph paper. This is because you may rely on the grid lines to make a reflection without doing any of the work yourself. Use plain white paper to actually exercise your skills if you need to.Thanks
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References
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