Question

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)
Please help me to solve this and no spams please or else the answer will be reported ​

Answer 1

We are going to find distance between sides

B (5 – 1)2+(4 – 2) = 16 + 4 = v20 = 2/5 AB V(3 5)2 + (8 4)2 = 4+ 16 = v20 = 2/5

CD = 2/5 V (-1 – 3)2 + (6 8)2 = V16 + 4 = V20

DA = V(1 +1)2 + (2-6)2 = V4+ 16 20 = 2/5

.:. AB = BC= CD = DA

Now, we are going to find distance between

diagonals.

AC = V(3 – 1)2 + (6 – 2)2 V4+ 16 = v20 = 2/5 BD= V(-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.

Answer 2

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