Step 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?

Let the point be $\"\"$ . $\"\"$

The complete rotation is $\"\"$ . $\"\"$ $\"\"$

The point is rotated $\"\"$ counter clock wise.

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

$\"\"$

$\"\"$ .

The new coordinate $\"\"$ .

The new coordinates after rotated $\"\"$ counter clock wise is $\"\"$ .

The rotation is equal in clock wise direction is $\"\"$ .

The coordinates will have the same $\"\"$ value and only change in the $\"\"$ value from positive to negative.

Simple, take the degrees of the circle and minus it by 90. 360 - 90 = 270 degrees.

Set x\\' = -y and y\\' = x \ \ \ \ where a\\' denotes the new coordinate. \ \ \ \ This is equivalent to a 270 degree clockwise rotation.

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?

Let the point be $\"\"$ .

The complete rotation is $\"\"$ . $\"\"$ $\"\"$

The point is rotated $\"\"$ counter clock wise.

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

$\"\"$

$\"\"$ .

The new coordinate is $\"\"$ .

The new coordinate $\"\"$ .

The new coordinates after rotated $\"\"$ counter clock wise is $\"\"$ .

The rotation is equal in clock wise direction is $\"\"$ .

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’?

The end points of the line segment are $\"\"$ and $\"\"$ .

The points are dialeted new end points are $\"\"$ and $\"\"$ . $\"\"$

Scale factor:

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 $\"\"$ .

$\"\"$

$\"\"$ .

The scale factor is $\"\"$ .

The length of the $\"\"$ is $\"\"$ .

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

Let the point be $\"\"$ . $\"\"$

The complete rotation is $\"\"$ . $\"\"$ $\"\"$

The point is rotated $\"\"$ counter clock wise.

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

$\"\"$

$\"\"$ .

The new coordinate $\"\"$ .

The new coordinates after rotated $\"\"$ counter clock wise is $\"\"$ .

The rotation is equal in clock wise direction is $\"\"$ .