SOLUTION: show that the points (-2,5), (-2,-1) and (4,-1) all lie on a circle whose <s>radius</s> CENTER is at (1,2). Find the length of the radius.

Algebra ->  Length-and-distance -> SOLUTION: show that the points (-2,5), (-2,-1) and (4,-1) all lie on a circle whose <s>radius</s> CENTER is at (1,2). Find the length of the radius.       Log On


   

Question 963688: show that the points (-2,5), (-2,-1) and (4,-1) all lie on a circle whose radius CENTER is at (1,2). Find the length of the radius.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Show that the distance from (1,2) to each of the three other given points is the same size.

Simplify each of these to show equality:

sqrt%28%28-2-1%29%5E2%2B%285-2%29%5E2%29
sqrt%28%283%29%5E2%2B%283%29%5E2%29

AND

sqrt%28%28-2-1%29%5E2%2B%28-1-2%29%5E2%29
sqrt%28%283%29%5E2%2B%283%29%5E2%29

AND

sqrt%28%284-1%29%5E2%2B%28-1-2%29%5E2%29
sqrt%28%283%29%5E2%2B%283%29%5E2%29
sqrt%289%2B9%29
sqrt%2818%29
highlight%283sqrt%282%29%29, size of the radius.

Even without simplifying completely, the equal distances is verified.