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### Course: 6th grade (WNCP)>Unit 3

Lesson 6: Transformations

# 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?
• I think he was just identifying it as a trapezoid in a general sense. I did the same thing when I worked it out on my own.
• 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 would suggest looking up "equations of a line" and "slope-intercept form" on the KA search bar.
• 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
• You don't really solve "y=3-x." He just put the line on the graph. You can rewrite it as "y=-x+3." the "x" is the slope which is almost like the distance between two points. 3 is the y-intercept which you plot on the y-axis.
• Is a trapezoid essentially the same as a trapezium?
• Yes, they are the same thing, trapezium in British, trapezoid in American.
• Anyone else got the working wrong but the answer right?
• 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.
• I believe it is exclusive to Khan Academy, though I may be wrong.
• It says a quadrilateral so why is it a triangle?
• At what point do you see it as a triangle? He even stated at the end that it ends up as a trapezoid which is a quadrilateral.