Point A(-5,7) is rotated about 90 degrees of the origin. What are coordinates of A?
回答 (9)
2016-06-06 8:02 pm
90 degrees in which direction....clockwise or anticlockwise??
:)>
:)>
2016-06-07 7:17 am
rotating cw : (5 ; 7)
rotating ccw : (-5 ; -7)
rotating ccw : (-5 ; -7)
2016-06-07 1:29 am
90 degrees in which direction? clockwise? counter-clockwise?
THE POINT (-5, 7) IS BEING USED FOR THE FOLLOWING MATH PROBLEMS:
if the point is being rotated 90 degrees clockwise, the answer is (7, 5). the rule for rotating any point 90 degrees clockwise is (x, y) ----> (y, -x).
if the point is being rotated 90 degrees counter-clockwise, the answer is (-7, -5). the rule for rotating any point 90 degrees counter-clockwise is (x, y) ----> (-y, x).
i know you didn't ask this, but if the point is being rotated 180 degrees in any direction, the answer is (5, -7). the rule for rotating any point 180 degrees in any direction is (x, y) ----> (-x, -y).
THE POINT (-5, 7) IS BEING USED FOR THE FOLLOWING MATH PROBLEMS:
if the point is being rotated 90 degrees clockwise, the answer is (7, 5). the rule for rotating any point 90 degrees clockwise is (x, y) ----> (y, -x).
if the point is being rotated 90 degrees counter-clockwise, the answer is (-7, -5). the rule for rotating any point 90 degrees counter-clockwise is (x, y) ----> (-y, x).
i know you didn't ask this, but if the point is being rotated 180 degrees in any direction, the answer is (5, -7). the rule for rotating any point 180 degrees in any direction is (x, y) ----> (-x, -y).
2016-06-06 8:04 pm
The coordinates of A are (-5, 7), just as they were given.
If the rotation is counterclockwise, the image of A is (-7, -5).
If the rotation is counterclockwise, the image of A is (-7, -5).
2016-06-07 6:03 pm
(7,5) clockwise
2016-06-07 2:17 pm
Answer to the trick question: The coordinates of A are (-5,7). ← ANSWER ❶
The position of A after rotation becomes A', but the original A remains static.
Now to find A'
Slipping from the real plane to complex numbers and back makes this simple:
Multiplying a complex number by i rotates the point 90°(anticlockwise by convention), and i²=-1
(-5,7) ≡ -5+7i
Rotation: (-5+7i)i = -5i+7i² = -7-5i ≡ (-7,-5) = A' ← ANSWER ❷
The position of A after rotation becomes A', but the original A remains static.
Now to find A'
Slipping from the real plane to complex numbers and back makes this simple:
Multiplying a complex number by i rotates the point 90°(anticlockwise by convention), and i²=-1
(-5,7) ≡ -5+7i
Rotation: (-5+7i)i = -5i+7i² = -7-5i ≡ (-7,-5) = A' ← ANSWER ❷
2016-06-06 9:58 pm
Original coordinates: (-5 , 7)
Angle of roration 90
x-new = x*cos( θ )-ysin( θ ) , θ = 90
= -5cos(90) - 7sin(90)
x-new = (-5)(0)-(7)(1) = -7
y-new = x*sins( θ)+ycos( θ ) , θ = 90
= -5sin(90) + 7cos(90)
y-new = (-5)(1)+(7)(0) = -5
Coordinates after rotation (-7,-5)
Angle of roration 90
x-new = x*cos( θ )-ysin( θ ) , θ = 90
= -5cos(90) - 7sin(90)
x-new = (-5)(0)-(7)(1) = -7
y-new = x*sins( θ)+ycos( θ ) , θ = 90
= -5sin(90) + 7cos(90)
y-new = (-5)(1)+(7)(0) = -5
Coordinates after rotation (-7,-5)
2016-06-06 8:44 pm
Which way? I'll suppose CCW.
Then the "new" A is at (-7,-5).
Then the "new" A is at (-7,-5).
2016-06-06 8:05 pm
Well,
let's suppose counterclockwise .... (positive direction)
(0 -1)(-5)
(1 0)(7)
=
(-7)
(-5)
therefore, the image is the point A '(-7, -5) ... in this case... !! ;-)
hope it' ll help !!
let's suppose counterclockwise .... (positive direction)
(0 -1)(-5)
(1 0)(7)
=
(-7)
(-5)
therefore, the image is the point A '(-7, -5) ... in this case... !! ;-)
hope it' ll help !!
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