# Point A is at #(-8 ,-7 )# and point B is at #(-3 ,-4 )#. Point A is rotated #pi/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?

##### 2 Answers

The new coordinates are

#### Explanation:

The rotation of

The coordinates of

Distance

Distance

The distance has changed by

New coordinates of point A is (-8,7) and distance between points A and B has changed.

#### Explanation:

When point A is rotated Π/2 clockwise, it moves up and crosses X axis.

For, the original angle created by point A at origin with X axis was less than Π/2.

Now, the distance OA (where, O is origin) is a constant.

Let us designate A' as new position of point A, after rotating Π/2 clockwise.

So we get an isosceles triangle AA'O, where angle AOA' is Π/2.

An isosceles triangle having Π/2 as the angle at vertex, will cause base angles as Π/4.

Now base of the triangle AA'O cuts X axis. Let us designate this point as O'

In triangles A'O'O and AO'O, OO' is a common arm, ∠O'A'O = ∠O'AO =Π/4; for triangle A'OA is an isosceles triangle.

So, triangle A'O'O and triangle AO'O are equal in all respects.

Hence O'A'=O'A=7 units; for coordinate of A was (-8, -7).

So coordinate of A' will be (-8, +7).

Now, distance between two points in Cartesian Coordinates is

Original distance was

New distance is

Therefore, we can say that distance between points A and B has changed.