Can a triangle have interior angle measures as 30^o , 45^o, and 90^o ?

Can a triangle have the sides as 3 cm, 4 cm, and 6 cm?

Define the measures of angles opposite to equal sides in a triangle?

What is the measure of each angle of an equilateral triangle?

In which triangle all three sides are of equal measure?

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 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 90^o 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 180^o 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 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).

 

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 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).