If two sides of a square are the part of the straight lines
5x - 2y = 13 and 5x – 2y + 16 = 0 then find the area of the square
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How do I find the area of a square if two sides of a square are a part of the straight lines 5x-2y=13 and 5x-2y+16=0?
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2 Answers
Jan van Delden, MSc Math and still interested
Answered July 10, 2019
The given lines are parallel, both have normal vector:
[math]\begin{bmatrix} 5 \\ -2\end{bmatrix[/math]
All we need to do is find the distance between these lines.
The equations can be written as an inner product:
For some points on the first line and on the second line.
The vector describing the difference between those points will satisfy:
With
We should choose such that it points in the direction of this normal vector, because we need to choose points on the lines having minimal distance. A simple verification shows that we could simply take:
The squared length (norm) of this vector equals the requested area:
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