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Rotations and Dilations help?

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1.)How are the coordinates of the new point found if it is rotated 90° counterclockwise? How many degrees is that equivalent to if the rotation is clockwise?
 
2)How are the coordinates of the new point found if it is rotated 180° counterclockwise? How many degrees is that equivalent to if the rotation is clockwise?
 
3)Describe in your own words what a rotation is.

4)A triangle has coordinates A (1, 5), B (-2, 1) and C (0, -4). What are the new coordinates if the triangle is dilated with a scale factor of  1/5<!-- RspH:I -->

5)A line segment has endpoints P (3, 6) and Q (12, 18) and is dilated so that its new endpoints are P’ (2, 4) and Q’ (8, 12). What is the scale factor? If the length of PQ is 15, what is the length of P’Q’?

6)A triangle has coordinates A (1, 5), B (-2, 1) and C (0, -4). What are the new coordinates if the triangle is rotated 90° clockwise around the origin?

7)How are the coordinates of the new point found if it is rotated 270° counterclockwise? How many degrees is that equivalent to if the rotation is clockwise

8)How are the coordinates of the new point found if it is dilated with a scale factor of 3?  

9)Describe in your own words what a dilation is.

 

asked Nov 15, 2015 in GEOMETRY by dneesy Rookie

9 Answers

0 votes

(1)

Let the point be image.

The complete rotation is image.

The point is rotated image counter clock wise.

Rotation of axes:

When an equation of a conic section is rewritten in the image-plane by rotating the coordinate axes through image, the equation in xy - plane can be found using

image and image.

The new coordinates after rotation are image,

image.

image.

The new coordinates after rotation of  image counter clock wise is image.

The rotation is equal in clock wise direction is image.

answered Nov 16, 2015 by Sammi Mentor
edited Nov 16, 2015 by Sammi
0 votes

(2)

Let the point be image.

The complete rotation is image.

The point is rotated image counter clockwise.

Rotation of axes:

When an equation of a conic section is rewritten in the image-plane by rotating the coordinate axes through image, the equation in xy - plane can be found using

image and image.

The new coordinates after rotation are image,

image.

image.

The new coordinates after rotation of  image counter clockwise is image.

The rotation is equal in clockwise direction is image.

answered Nov 16, 2015 by Sammi Mentor
0 votes

Rotation:

The "rotation" transformation is where you turn a figure about a given point .

The point about which the object is rotated can be inside the figure or anywhere outside it.

The amount of rotation is called the angle of rotation and is measured in degrees.

By convention a rotation counter-clockwise is a positive angle, and clockwise is considered a negative angle. 

answered Nov 16, 2015 by cameron Mentor
0 votes

 

4)

Coordinates of triangle are and  .

Triangle is dilated with a scale factor of  image.

Dilation:

This is defined as either enlargement of reduction of a figure in plane movements.

If the scale factor is greater than , then it is said to be enlargement.

If the scale factor is between 0 and 1, then it is said to be reduction.

In either case of Dilation, the new point is given by .

Thus, new coordinates of the triangle are

image.

image.

image.

 

answered Nov 16, 2015 by cameron Mentor
edited Nov 16, 2015 by steve
0 votes

(5)

The end points of the line segment are image and image.

The new end points are image and image.

Scale factor:

If the scale factor is imagethen the new point  is .

Find the scale factor.

image

image

image.

The scale factor is image.

The length of the image is image.

The length of the image is image.

The length of the imageis image.

answered Nov 16, 2015 by Sammi Mentor
edited Nov 16, 2015 by Sammi
0 votes

(6)

A triangle has coordinates A (1, 5), B (-2, 1) and C (0, -4).

The point is rotated  clockwise around the origin.

The rotation is equal in counter clockwise direction is .

When an equation of a conic section is rewritten in the plane by rotating the coordinate axes through , the equation in -plane can be found using

 and .

The new coordinates after rotation are image,

image.

image.

The new coordinates after rotated  clockwise is image.

Thus, new coordinates of the triangle are imageimage and image.

answered Nov 16, 2015 by cameron Mentor
0 votes

(7)

Let the point be image.

The complete rotation is image.

The point is rotated image counter clockwise.

Rotation of axes:

When an equation of a conic section is rewritten in the image-plane by rotating the coordinate axes through image, the equation in xy - plane can be found using

image and image.

The new coordinates after rotation are image,

image.

image.

The new coordinates after rotation of  image counter clockwise are image.

The rotation in clockwise direction is image.

answered Nov 16, 2015 by Sammi Mentor
edited Nov 16, 2015 by Sammi
0 votes

(8)

Let the point be image.

Point is dilated with a scale factor of image.

Dilation:

If the coordinates of a point image are dilated with a scale factor of image then new point after dilation is image.

New coordinates of the point are image.

answered Nov 16, 2015 by cameron Mentor
0 votes

(9)

Dilation:

It is defined as either enlargement of reduction of a figure in plane movements.

If the scale factor is greater than , then it is said to be enlargement.

If the scale factor is between 0 and 1, then it is said to be reduction.

answered Nov 16, 2015 by cameron Mentor

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