Point A is at (3 ,2 ) and point B is at (-7 ,3 ). 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?

1 Answer
David G.
Mar 21, 2016

Rotating Point A (3, 2) clockwise through pi/2 yields Point A' (2, -3). We can then calculate the distance between Point A' and Point B as approximately 10.8 units.

Explanation:

Now, pi/2 is 1/4 of a full rotation (2pi) or 90^o. If we rotate the point (3, 2) through this angle clockwise, we move from the first to the fourth quadrant, so the x value will still be positive and the y value will be negative.

You should probably draw a diagram, but it turns out that the new point, which we can call Point A', has the coordinates (2, -3).

We can calculate the distance between Point A' and Point B:

r=sqrt((x_2-x_1)^2+(y_2-y_1)^2)=sqrt(((-7)-2)^2+(3-(-3))^2)=sqrt(81+36)~~10.8

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