Question

if the axes are rotated through an angle 45 the coordinates of (2✓2-3✓2) in the new system are​

Answer 1

Answer:

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Answer 2

If the axes are rotated through an angle 45 the coordinates of (2✓2,-3✓2) in the new system are​ ( 0.5, -3.5).

Given the point x = 2√2  y = -3√2

Ф = 45°

We need to find

• x' = xcosФ - ysinФ and
• y' = ycosФ + xsinФ

Therefore,

• x' = 2√2 = xcos45° - ysin45°
• 2√2 = x(1/√2) - y(1/√2) = = >
• x - y =4 -- (1)

Also,

• y' = -3√2 = ycos45° + xsin45°
• -3√2 = y(1/√2) + x1/√2) = = >
• x + y = -3 --(2)

Adding ( 1 ) and ( 2 ) == >

• 2x = 1 ==> x =0.5

• y = x - 4 = 0.5 - 4 = - 3.5

Therefore coordinates in the new system are (0. 5 , -3.5).