Question

Consider the square a(1,0), b(0,0), c(0,1), d(1,1). Rotate the square abcd by 45o clockwise about a(1,0).

Answer 1

a = (1, 0) , b = ((√2  - 1)/√2  , 1/√2) ,  c = (1 , √2) , d = ((√2  + 1)/√2  , 1/√2)

Step-by-step explanation:

a(1,0), b(0,0), c(0,1), d(1,1)

Each Side length = 1

Rotated 45° clock wise

Hence slope of ad would be Tan45° = 1

y = x  + c

passing through (1,0)

=> 0 = 1 + c

=> c = - 1

y = x - 1

also (x - 1)² + y²  = 1

=> y² + y²  = 1

=> 2y² = 1

=> y² = 1/2

=> y  = 1/√2

1/√2  = x - 1

=> x = 1 + 1/√2

=> x = (√2  + 1)/√2

Hence d = ((√2  + 1)/√2  , 1/√2)

Slope of ab would be - 1 (tan 135°)

y = -x  + c

passing through (1,0)

=> 0 = -1 + c

=> c =  1

y = -x + 1

=> (x - 1) = - y

also (x - 1)² + y²  = 1

=> (-y)² + y²  = 1

=> 2y² = 1

=> y² = 1/2

=> y  = 1/√2

1/√2  = -x + 1

=> x = 1 - 1/√2

=> x = (√2  - 1)/√2

Hence b = ((√2  - 1)/√2  , 1/√2)

slope of ab =  (1/√2)/(-1/√2) = -1

Slope of bd = 1   =>  bd

a = (1, 0)

b = ((√2  - 1)/√2  , 1/√2)

c = (1 , √2)

d = ((√2  + 1)/√2  , 1/√2)

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