Points with distance 5 from the point (-2, -1)

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Question from Alexa, a student:

I know the answer to the question, (I looked it up in the back of the book) but I need to know how to get the answer.

Problem:
Find all points having a x-coordinate of 2 whose distance from the point (-2, -1) is 5.

Hi Alexa,

In my mind I see a diagram. The points in the plane that are 5 units from (-2, -1) make up the circle with center (-2, -1) and radius 5. You want the points on this circle with x-coordinate 2, the points labeled P and Q in the diagram.

diagram

I then added a point R to complete the right triangle PCR.

diagram

What does Pythagoras tell you?

Write back if you need more assistance,
Penny

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