Question
In the given figure, 
is the sum of _____________
- Angle a and Angle c
- Angle b and Angle c
- Angle a and Angle b and Angle c
- Angle a and Angle b
Hint:
is the sum of opposite interior angles
The correct answer is: Angle a and Angle b
From the given figure;
is the sum of opposite interior angles
is the sum of Angle a and Angle b
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Find the vertices of each of the figures of rotation 900 counter-clockwise about the origin
Given Data:
>>From figure, the vertices of the triangle are:
B(-5,0) and E(-2,1) and G(-2, -3).
>>>let, the point (x, y) be in the space and the Angle of Rotation becomes 
= 90.
>>>new coordinates are:
= (x cos - y sin , y cos + x sin)
= (x cos90 -y sin90 , y cos90 + x sin90)
= (-y, x).
* Hence, the final coordinates after rotation through 90 degrees counter clockwise are (-y, x).
>>>Similarly, for the coordinates B(-5,0) and E(-2,1) and G(-2, -3) the rotation of points through 90 degrees counter clock wise becomes:
B(0,-5) and E(3, -2) and G(3,2).
***Therefore, the coordinates of triangle B(-5,0) and E(-2,1) and G(-2, -3) after rotation through 90 degrees counter clockwise becomes B(0,-5) and E(3, -2) and G(3,2).
Find the vertices of each of the figures of rotation 900 counter-clockwise about the origin
Given Data:
>>From figure, the vertices of the triangle are:
B(-5,0) and E(-2,1) and G(-2, -3).
>>>let, the point (x, y) be in the space and the Angle of Rotation becomes = 90.
>>>new coordinates are:
= (x cos - y sin , y cos + x sin)
= (x cos90 -y sin90 , y cos90 + x sin90)
= (-y, x).
* Hence, the final coordinates after rotation through 90 degrees counter clockwise are (-y, x).
>>>Similarly, for the coordinates B(-5,0) and E(-2,1) and G(-2, -3) the rotation of points through 90 degrees counter clock wise becomes:
B(0,-5) and E(3, -2) and G(3,2).
***Therefore, the coordinates of triangle B(-5,0) and E(-2,1) and G(-2, -3) after rotation through 90 degrees counter clockwise becomes B(0,-5) and E(3, -2) and G(3,2).
Find the vertices of each of the figure of rotation 900 clockwise about the origin
Given Data:
* From figure, the points are K(2, -2) and U(3, 3) and T(5, 0) are the vertices of the triangle.
>>Let (x, y) be the point in the space and angle of rotation becomes = -90 degrees.
*Then, the new coordinates are :
= (x cos - y sin , y cos + x sin)
= (x cos(-90) -y sin(-90) , y cos(-90) + x sin(-90))
= (y, -x).
>>Then, the new coordinates are (y, -x).
>>>Similarly, the rotation of triangular vertices K(2, -2) and U(3, 3) and T(5, 0) through 90 degrees clockwise becomes :
K(-2, -2) and U(3, -3) and T(0, -5).
*Therefore, the vertices K(2, -2) and U(3, 3) and T(5, 0) after rotation through 90 degrees clockwise becomes K(-2, -2) and U(3, -3) and T(0, -5).
Find the vertices of each of the figure of rotation 900 clockwise about the origin
Given Data:
* From figure, the points are K(2, -2) and U(3, 3) and T(5, 0) are the vertices of the triangle.
>>Let (x, y) be the point in the space and angle of rotation becomes = -90 degrees.
*Then, the new coordinates are :
= (x cos - y sin , y cos + x sin)
= (x cos(-90) -y sin(-90) , y cos(-90) + x sin(-90))
= (y, -x).
>>Then, the new coordinates are (y, -x).
>>>Similarly, the rotation of triangular vertices K(2, -2) and U(3, 3) and T(5, 0) through 90 degrees clockwise becomes :
K(-2, -2) and U(3, -3) and T(0, -5).
*Therefore, the vertices K(2, -2) and U(3, 3) and T(5, 0) after rotation through 90 degrees clockwise becomes K(-2, -2) and U(3, -3) and T(0, -5).
Find the vertices of each of the figure of rotation 1800 about the origin
Given Data:
>>From figure, the coordinates of the points w, u, x are.
>>> W(-4, -3) and U(4, 0) and X(-3, -2) are the required coordinates of a triangle.
>>Let, (x, y) be the point in the space and are rotated through 180 degrees.
Then, the new coordinates are:
= (x cos - y sin , y cos + x sin)
= (x cos180 -y sin180 , y cos180 + xsin180)
= (-x , -y)
* Then, the new coordinates of (x, y) after rotation through 180 degrees is (-x, -y).
>>>Similarly, for W(-4, -3) and U(4, 0) and X(-3, -2) the new coordinates are:
W(4, 3) and U(-4, 0) and (3, 2).
>>>Hence, the rotation of points W(-4, -3) and U(4, 0) and X(-3, -2) through 180 degrees becomes W(4, 3) and U(-4, 0) and (3, 2).
Find the vertices of each of the figure of rotation 1800 about the origin
Given Data:
>>From figure, the coordinates of the points w, u, x are.
>>> W(-4, -3) and U(4, 0) and X(-3, -2) are the required coordinates of a triangle.
>>Let, (x, y) be the point in the space and are rotated through 180 degrees.
Then, the new coordinates are:
= (x cos - y sin , y cos + x sin)
= (x cos180 -y sin180 , y cos180 + xsin180)
= (-x , -y)
* Then, the new coordinates of (x, y) after rotation through 180 degrees is (-x, -y).
>>>Similarly, for W(-4, -3) and U(4, 0) and X(-3, -2) the new coordinates are:
W(4, 3) and U(-4, 0) and (3, 2).
>>>Hence, the rotation of points W(-4, -3) and U(4, 0) and X(-3, -2) through 180 degrees becomes W(4, 3) and U(-4, 0) and (3, 2).
What will be the coordinates of the image of ABC with points A (-3,4) B (0, 1), C (-5, 2) after it is rotated 90o counter-clockwise about the origin?
Given That:
A (-3,4) B (0, 1), C (-5, 2) are the vertices of a triangle.
>>>The vertices of a triangle are rotated through 90 degrees counter clockwise direction.
>>>Let, the point on the space be (x, y). Then Angle of Rotation becomes 90 degrees.
>>>Hence, new coordinates are:
= (x cos - y sin , y cos + x sin)
= (x cos90 - y sin90 , y cos90 + x sin90)
= (-y , x).
>>>Similarly, the rotation of the points A (-3,4) B (0, 1), C (-5, 2) becomes:
A(-4,-3) and B(-1,0) and C(-2, -5).
***Therefore, the triangle vertices A (-3,4) B (0, 1), C (-5, 2) after rotation through 90 degrees counter clockwise are A(-4,-3) and B(-1,0) and C(-2, -5).
What will be the coordinates of the image of ABC with points A (-3,4) B (0, 1), C (-5, 2) after it is rotated 90o counter-clockwise about the origin?
Given That:
A (-3,4) B (0, 1), C (-5, 2) are the vertices of a triangle.
>>>The vertices of a triangle are rotated through 90 degrees counter clockwise direction.
>>>Let, the point on the space be (x, y). Then Angle of Rotation becomes 90 degrees.
>>>Hence, new coordinates are:
= (x cos - y sin , y cos + x sin)
= (x cos90 - y sin90 , y cos90 + x sin90)
= (-y , x).
>>>Similarly, the rotation of the points A (-3,4) B (0, 1), C (-5, 2) becomes:
A(-4,-3) and B(-1,0) and C(-2, -5).
***Therefore, the triangle vertices A (-3,4) B (0, 1), C (-5, 2) after rotation through 90 degrees counter clockwise are A(-4,-3) and B(-1,0) and C(-2, -5).
What will be the coordinates of the image of ABC with points A (-3,4) B (0, 1), C (-5, 2) after it is rotated 180o about the origin?
Given That:
A (-3,4), B(0, 1), C (-5, 2) are the points of triangle.
>>we re asked to rotate the vertices of triangle by 180 degrees.
>>>let, the point be (x, y) then the angle of rotation be 180 degrees. Then:
>>New Coordinates are:
= (x cos - y sin , y cos + x sin).
= (x cos180 - y sin180 , y cos180 + x sin180)
= (-x , -y).
>>>Hence, any point that rotated by 180 degrees will just change the sign of the coordinates.
>>>Similarly, for triangle coordinates A (-3,4), B(0, 1), C (-5, 2) the rotation through 180 degrees about origin becomes : A(3, -4) and B(0, -1) and C(5, -2).
What will be the coordinates of the image of ABC with points A (-3,4) B (0, 1), C (-5, 2) after it is rotated 180o about the origin?
Given That:
A (-3,4), B(0, 1), C (-5, 2) are the points of triangle.
>>we re asked to rotate the vertices of triangle by 180 degrees.
>>>let, the point be (x, y) then the angle of rotation be 180 degrees. Then:
>>New Coordinates are:
= (x cos - y sin , y cos + x sin).
= (x cos180 - y sin180 , y cos180 + x sin180)
= (-x , -y).
>>>Hence, any point that rotated by 180 degrees will just change the sign of the coordinates.
>>>Similarly, for triangle coordinates A (-3,4), B(0, 1), C (-5, 2) the rotation through 180 degrees about origin becomes : A(3, -4) and B(0, -1) and C(5, -2).
In what quadrant will an image be if the figure is in quadrant I and is rotated 90° counter clockwise?
* 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).
In what quadrant will an image be if the figure is in quadrant I and is rotated 90° counter clockwise?
* 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).
In what quadrant will an image be if the figure is in quadrant II and is rotated 180° clockwise?
* 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).
In what quadrant will an image be if the figure is in quadrant II and is rotated 180° clockwise?
* 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).
In what quadrant will an image be if the figure is in quadrant III and is rotated 90° clockwise?
* 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).
In what quadrant will an image be if the figure is in quadrant III and is rotated 90° clockwise?
* 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).
If the point (-4, -6) rotates 180° counter-clockwise, then the point will be
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).
If the point (-4, -6) rotates 180° counter-clockwise, then the point will be
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).
