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## High school geometry

### Course: High school geometry>Unit 2

Lesson 4: Symmetry

# Finding a quadrilateral from its symmetries

Two of the points that define a certain quadrilateral are (0,9) and (3,4). The quadrilateral has reflective symmetry over the line y=3-x. Draw and classify the quadrilateral. Created by Sal Khan.

## Want to join the conversation?

• Why would it not be an isosceles trapezoid? • Sometimes it's difficult to see the perpendicular to the line of reflection. Therefore, I've been using the following technique: plot the "transform" (I don't know the correct terminology) of the point [e.g. if the point is (0,9), then plot (-9,0) OR if the point is (3,4), then plot (-4,-3)] then move the point to the final, correct reflection in both the x & y directions using the x-intercept & y-intercept of the line of reflection as offsets. In the same example, (-9,0) will move +3 in the x-direction since the x-intercept of the line of reflection is +3 and also move +3 in the y-direction since the y-intercept is also +3 to the final reflection point of (-6,3) and for the point at (3,4), the final reflection point is (-4+3, -3+3) or (-1,0). Is this true in all cases? Even if the reflection isn't over a straight line but perhaps some other 2-dimensional shape such as a circle? • Well the math is a little more complicated when the slope of the line isn't `1` or `-1`, but yes, you can use the perpendicular line (which has a slope of `-1/m` compared to the original line's slope of `m`) to calculate the reflected point mathematically.
• At Sal talks about "when x is 0, y is 3 - that's our y intercept" and then talks about how the slope goes down from there. I've been following everything I can on geometry but I seemed to have missed exactly how these slopes work. Is there another unit I can look at that describes how the whole y = 3 - x thing works? • I do not know how to solve Y=3-X. I did not find any explanation about it in previous videos in this section. Could you explain it to me please?

Monir • Is a trapezoid essentially the same as a trapezium? • It says a quadrilateral so why is it a triangle? • Where is the widget to make polygons? I tried finding it on the site in vain. I need either (1) a URL or (2) search keywords that will yield very few results that include what I'm looking for. • Anyone else got the working wrong but the answer right? • I realize this is a simple reflection line with a slope of -1, however if the coefficient was different so that perhaps it was a steeper slope, would we know what is perpendicular by taking the opposite reciprocal of the slope and then just shifting up or down and right or left so many units based on that calculation? For example, let's say the line we are reflecting over is y = -2/3x-2. A line perpendicular to this one would have a slope of +3/2. We would then use up 3 units and to the right 2 units as a measurement to determine a point's reflection across the original line (or work backwards if the point was above the line), counting how many units we have moved to get to the line of reflection? I'm fairly bad at visualizing reflections, etc. and I have to take an important math test where I cannot write anything down so I am attempting to see if this is a correct method that I can use in my head when I am challenged with this no-writing test. Thank you! • Why are two of the lines parallel? 