Question
If the point (-4, -6) rotates 180° counter-clockwise, then the point will be
- (4, 6)
- (-4, 6)
- (4, -6)
- (-6, -4)
Hint:
Rotate the given point through 180 degrees counter clockwise and obtain the new coordinates.
The correct answer is: (4, 6)
Given Data:
If the point (-4, -6) rotates 180° counter-clockwise, then the point will be
>>>Since it is counter clockwise the angle of rotation becomes 
= 180 degrees.
>>Point (x, y) = (-4, -6)
>>>New Coordinates are:
= (x cos - y sin , y cos + x sin).
= (-4cos180 + 6sin180 , -6cos180 -6sin180)
= (4 , 6).
***Therefore, the rotation of the point (-4, -6 ) through 180 degrees counter clockwise becomes (4, 6).
* In Mathematics, rotation means the Circular movement of an object around one fixed point.
* In rotation, the image after transformation remains constant.
* Hence, it is called as a rigid transformation.
* No Change in shape and size.
* The Shape rotates counter- clockwise when the degrees is positive and rotates clockwise when degrees is negative.
*The Rotation of a point (x, y) about origin and through angle alpha, then:
New coordinates of a point (x, y) after it's rotation becomes (x cos - y sin , y cos + x sin).
Related Questions to study
If the point (4, 6) rotates 90° counter-clockwise, then the point will be
Given Data:
If the point (4, 6) rotates 90° counter-clockwise, then the point will be
>>>Since, it is counter clockwise rotation angle of rotation becomes = 90 degrees.
>>point (x, y)= (4, 6)
*New Coordinates are:
= (x cos - y sin , y cos + x sin).
= (4cos90 - 6sin90 , 6cos90 + 4sin90)
= (-6 , 4).
***The rotation of the point (4, 6 ) through 90 degrees counter clockwise becomes (-6, 4).
If the point (4, 6) rotates 90° counter-clockwise, then the point will be
Given Data:
If the point (4, 6) rotates 90° counter-clockwise, then the point will be
>>>Since, it is counter clockwise rotation angle of rotation becomes = 90 degrees.
>>point (x, y)= (4, 6)
*New Coordinates are:
= (x cos - y sin , y cos + x sin).
= (4cos90 - 6sin90 , 6cos90 + 4sin90)
= (-6 , 4).
***The rotation of the point (4, 6 ) through 90 degrees counter clockwise becomes (-6, 4).
If the point (2, 3) rotates 90°clockwise, then the point will be
Given data:
If the point (2, 3) rotates 90°clockwise, then the point will be
>>>Since, it is clockwise rotation angle of rotation becomes negative that is = -90.
>>And the point (x, y) = (2, 3).
>>>Hence, the new coordinates are:
= (x cos - y sin , y cos + x sin).
= (2 cos(-90) - 3 sin(-90) , 3 cos(-90) + 2 sin(-90))
= (3 ,-2).
**Hence, the rotation of the point (2, 3) through 90 degrees clockwise is (3, -2).
If the point (2, 3) rotates 90°clockwise, then the point will be
Given data:
If the point (2, 3) rotates 90°clockwise, then the point will be
>>>Since, it is clockwise rotation angle of rotation becomes negative that is = -90.
>>And the point (x, y) = (2, 3).
>>>Hence, the new coordinates are:
= (x cos - y sin , y cos + x sin).
= (2 cos(-90) - 3 sin(-90) , 3 cos(-90) + 2 sin(-90))
= (3 ,-2).
**Hence, the rotation of the point (2, 3) through 90 degrees clockwise is (3, -2).
In rotation, the point (x, y) after moving 180° both clockwise and anti-clockwise will be
Given Data:
In rotation, the point (x, y) after moving 180° both clockwise and anti-clockwise will be
>>First step is to rotate the point (x, y) through 180 degrees clockwise.
* Hence, the angle of rotation becomes = -180
The new coordinates are:
= (x cos - y sin , y cos + x sin)
= (x cos(-180) - y sin(-180) , y cos(-180) + x sin(-180))
= (-x, -y).
***Therefore, the rotation of a point (x, y) through 180 degrees clockwise gives (-x, -y).
>>>similarly, the rotation of the point (x, y) through 180 degrees counter clockwise gives:
*The new Coordinates are:
= (x cos - y sin , y cos + x sin)
= (x cos(180) -y sin(180) , y cos(180) + x sin(180))
= (-x , -y).
***Therefore, the rotation of the point (x, y) through 180 degrees counter clockwise gives (-x, -y)
>>>Hence, we can say that the rotation of the point (x, y) through any direction yields (-x, -y).
In rotation, the point (x, y) after moving 180° both clockwise and anti-clockwise will be
Given Data:
In rotation, the point (x, y) after moving 180° both clockwise and anti-clockwise will be
>>First step is to rotate the point (x, y) through 180 degrees clockwise.
* Hence, the angle of rotation becomes = -180
The new coordinates are:
= (x cos - y sin , y cos + x sin)
= (x cos(-180) - y sin(-180) , y cos(-180) + x sin(-180))
= (-x, -y).
***Therefore, the rotation of a point (x, y) through 180 degrees clockwise gives (-x, -y).
>>>similarly, the rotation of the point (x, y) through 180 degrees counter clockwise gives:
*The new Coordinates are:
= (x cos - y sin , y cos + x sin)
= (x cos(180) -y sin(180) , y cos(180) + x sin(180))
= (-x , -y).
***Therefore, the rotation of the point (x, y) through 180 degrees counter clockwise gives (-x, -y)
>>>Hence, we can say that the rotation of the point (x, y) through any direction yields (-x, -y).
In rotation, the point (x, y) after moving 270° clockwise and 90° counter-clockwise will be
Given Data:
In rotation, the point (x, y) after moving 270° clockwise and 90° counter-clockwise will be
>>>The first step is to rotate a point (x, y) through 270 degrees clockwise
* Angle of rotation becomes -270
* Then, the coordinates after rotation :
= (x cos - y sin , y cos + x sin)
= (x cos(-270) - y sin(-270) , y cos(-270) + x sin(-270))
= (-y, x).
>>>Second step is to rotate (-y, x) through 90 degrees counter clockwise
* Angle of rotation becomes 90 degrees.
* Then , the new coordinates after rotation becomes:
= (x cos - y sin , y cos + x sin)
= (-y cos(90) - x sin(90) , x cos(90) -y sin(90))
= (-x , -y).
***Therefore the rotation of a point (x, y) through 270 degrees clockwise and 90 degrees counter clockwise becomes (-x, -y).
In rotation, the point (x, y) after moving 270° clockwise and 90° counter-clockwise will be
Given Data:
In rotation, the point (x, y) after moving 270° clockwise and 90° counter-clockwise will be
>>>The first step is to rotate a point (x, y) through 270 degrees clockwise
* Angle of rotation becomes -270
* Then, the coordinates after rotation :
= (x cos - y sin , y cos + x sin)
= (x cos(-270) - y sin(-270) , y cos(-270) + x sin(-270))
= (-y, x).
>>>Second step is to rotate (-y, x) through 90 degrees counter clockwise
* Angle of rotation becomes 90 degrees.
* Then , the new coordinates after rotation becomes:
= (x cos - y sin , y cos + x sin)
= (-y cos(90) - x sin(90) , x cos(90) -y sin(90))
= (-x , -y).
***Therefore the rotation of a point (x, y) through 270 degrees clockwise and 90 degrees counter clockwise becomes (-x, -y).
In rotation, the point (x, y) after moving 270° clockwise will be
Given Data:
In rotation, the point (x, y) after moving 270° clockwise will be
>>>since, it is clockwise rotation the angle of rotation becomes negative.
>>= -270.
>>>New coordinates of a point after rotation:
= (x cos - y sin , y cos + x sin)
= (x cos(-270) - y sin(-270) , y sin(-270) + x sin(-270))
= (-y , x).
***Hence, the rotation of the point (x, y) through 270 degrees clockwise becomes (-y, x)
In rotation, the point (x, y) after moving 270° clockwise will be
Given Data:
In rotation, the point (x, y) after moving 270° clockwise will be
>>>since, it is clockwise rotation the angle of rotation becomes negative.
>>= -270.
>>>New coordinates of a point after rotation:
= (x cos - y sin , y cos + x sin)
= (x cos(-270) - y sin(-270) , y sin(-270) + x sin(-270))
= (-y , x).
***Hence, the rotation of the point (x, y) through 270 degrees clockwise becomes (-y, x)
In rotation, the point (x, y) after moving 180°counter-clockwise will be
Given That:
In rotation, the point (x, y) after moving 180°counter-clockwise will be
>>>Since, it is counter clockwise rotation the angle of rotation remains positive.
>>>Therefore, the angle of rotation becomes 180 degrees.
>>>The new coordinates becomes:
= (x cos - y sin , y cos + x sin)
= (x cos(180) -y sin(180) , y cos(180) + x sin(180))
= (-x , -y).
***Hence, the rotation of the point (x, y) through 180 degrees counter clockwise becomes (-x, -y).
In rotation, the point (x, y) after moving 180°counter-clockwise will be
Given That:
In rotation, the point (x, y) after moving 180°counter-clockwise will be
>>>Since, it is counter clockwise rotation the angle of rotation remains positive.
>>>Therefore, the angle of rotation becomes 180 degrees.
>>>The new coordinates becomes:
= (x cos - y sin , y cos + x sin)
= (x cos(180) -y sin(180) , y cos(180) + x sin(180))
= (-x , -y).
***Hence, the rotation of the point (x, y) through 180 degrees counter clockwise becomes (-x, -y).
In rotation, the point (x, y) after moving 180° clockwise will be
Given Data:
In rotation, the point (x, y) after moving 180° clockwise will be
>>> Since, the clockwise rotation denotes negative degrees the angle of rotation becomes -180 degrees.
>>>New Coordinates of a point (x, y) are:
= (x cos - y sin , y cos + x sin)
= (x cos(-180) - y sin(-180) , y cos(-180) + x sin(-180))
= (-x , -y).
**Therefore, the rotation of the point (x, y) through 180 degrees clockwise gives (-x , -y).
In rotation, the point (x, y) after moving 180° clockwise will be
Given Data:
In rotation, the point (x, y) after moving 180° clockwise will be
>>> Since, the clockwise rotation denotes negative degrees the angle of rotation becomes -180 degrees.
>>>New Coordinates of a point (x, y) are:
= (x cos - y sin , y cos + x sin)
= (x cos(-180) - y sin(-180) , y cos(-180) + x sin(-180))
= (-x , -y).
**Therefore, the rotation of the point (x, y) through 180 degrees clockwise gives (-x , -y).
In rotation, the point (x, y) after moving 90° counter-clockwise will be
Given That:
In rotation, the point (x, y) after moving 90° counter-clockwise will be
* We were asked to rotate the point (x, y) through 90 degrees counter clockwise.
>Hence, the point after rotation becomes:
= (x cos - y sin , y cos + x sin)
= (x cos(90) - y sin(90) , y cos(90) + x sin(90))
= (-y , x ).
>>>Hence, the rotation of the point (x, y) through 90 degrees counter clockwise becomes (-y, x).
In rotation, the point (x, y) after moving 90° counter-clockwise will be
Given That:
In rotation, the point (x, y) after moving 90° counter-clockwise will be
* We were asked to rotate the point (x, y) through 90 degrees counter clockwise.
>Hence, the point after rotation becomes:
= (x cos - y sin , y cos + x sin)
= (x cos(90) - y sin(90) , y cos(90) + x sin(90))
= (-y , x ).
>>>Hence, the rotation of the point (x, y) through 90 degrees counter clockwise becomes (-y, x).
In rotation, the point (x, y) after moving 90° clockwise will be
Given That:
In rotation, the point (x, y) after moving 90° clockwise will be
>>point (x, y) will present in the 1st Quadrant.
>>Since, to rotate the point in clockwise denotes backward movement of point.
>> hence, the point is rotated to fourth Quadrant and the point changes to (y, -x).
>>>Final point obtained on rotation of (x, y) by 90 degrees clockwise is (y, -x).
In rotation, the point (x, y) after moving 90° clockwise will be
Given That:
In rotation, the point (x, y) after moving 90° clockwise will be
>>point (x, y) will present in the 1st Quadrant.
>>Since, to rotate the point in clockwise denotes backward movement of point.
>> hence, the point is rotated to fourth Quadrant and the point changes to (y, -x).
>>>Final point obtained on rotation of (x, y) by 90 degrees clockwise is (y, -x).
In rotation, images after transformation will be
Hence, we can say that the image or object transformation in rotation will be equal.
In rotation, images after transformation will be
Hence, we can say that the image or object transformation in rotation will be equal.
Rotation is transformation that
Hence, we can say that rotation is the transformation that rotates about a point.
Rotation is transformation that
Hence, we can say that rotation is the transformation that rotates about a point.
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