The vertices of a square are located at (a, 0), (a, a), (0, a), and (0, 0). What is the length of a diagonal?

slaggingV

slaggingV

Answered question

2021-01-02

The vertices of a square are located at (a, 0), (a, a), (0, a), and (0, 0). What is the length of a diagonal?

Answer & Explanation

hosentak

hosentak

Skilled2021-01-03Added 100 answers

Let we name the vertices of square as O(0,0) ,A(a,0), C(a,a) and D(0,a)
When we join vertex O and C by line segment we find CO as the length of diagonal.
Similarly when we join vertex A and D by line segment we find DA as the length of diagonal.
Distance between any two arbitrary coordinates E(x1,y1) and F(x2,y2)=((x2x1)2+(y2y1)2)
Distance between CO=((a0)2+(a0)2)
CO=((a2)+(a2))=(2a2)=a2
Distance between DA=((0a)2+(a0)2)
DA=((a)2+(a)2)=2a2=a2
Thus the length of diagonal is a2

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