Chi N.
asked • 03/20/23Geometry Help for classifying a shape as a quadrilateral.
Let us say that we have shape LMNO, located at L(1,1), M(4,4) N(7,1) and O(4,-2). How can I classify this as a quadrilateral with coordinate geometry.
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1 Expert Answer
Doug C. answered • 03/20/23
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A diagram will help determine a strategy for identifying the type of quadrilateral.
The diagram will show that the quadrilateral sort of looks like a square, but how to prove it?
Try finding the length of each side by using the distance formula. If all the sides are equal then it is for sure a rhombus and might be a square.
To determine if it is a square, calculate the slopes of two adjacent sides. If those slopes are negative reciprocals, then the angle is a right angle, which means a square.
This Desmos graph can be used to check your work:
desmos.com/calculator/ic6gtegmva
Chi N.
And the distance formula would result in 4.24 for all sides, correct? Making it a square.
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03/20/23
Doug C.
Or an exact value 3sqrt(2), so yes after showing right angle, you can deduce a square.
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03/20/23
Chi N.
??? In my workings I got: This for side LM: (x2-x1)^2 + (y2-y1)^2 (4-1)^2 + (4-1)^2 (3)^2 + (3)^2 9+9 18 then sqrt of 18= 4.24 For 3sqrt(2), did you mean the point after I subtracted?
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03/20/23
Doug C.
Everything you did was correct. sqrt(18) = sqrt[9(2)] = sqrt(9)sqrt(2) = 3sqrt(2). If you check the Desmos graph you will see line 11 shows 3sqrt(2) as 4.24264...
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03/20/23
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Mark M.
Did you draw and label a diagram?03/20/23