Show from the gradients that the points (4,1),(1,2),(2,5) and (5,4) are the vertices of a square.
(This question is from the chapter Co-ordinate geometry)
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Answered by
0
Answer:
We are going to find distance between sides
AB=
(5−1)
2
+(4−2)
2
=
16+4
=
20
=2
5
BC=
(3−5)
2
+(8−4)
2
=
4+16
=
20
=2
5
CD=
(−1−3)
2
+(6−8)
2
=
16+4
=
20
=2
5
DA=
(1+1)
2
+(2−6)
2
=
4+16
=
20
=2
5
∴ AB=BC=CD=DA
Now, we are going to find distance between diagonals.
AC=
(3−1)
2
+(6−2)
2
=
4+16
=
20
=2
5
BD=
(−1+5)
2
+(6−4)
2
=
16+4
=
20
=2
5
∴ AC=BD
So, here we can see distance between all sides and diagonals are equal.
∴ Points A,B,C and D are the vertices of a square
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