On the Cartesian plane in which each unit is one foot, a dog is tied to a post on the point (4,3) by a 10 foot rope. What is the greatest distance the dog can be from the origin?
+71 Well first we have to find the distance from the origin to the point (4,3). Now to do this we use the distance formula.
I didnt want to type this out so i found a picture. Now the origin point is (0,0) So now we have two points we can plug in to find the difference between them. Now the X1 and X2 aswell as y1 and y2 are interchangable within their brackets. So \(D=\sqrt{(4)^2 + (3)^2}\) Which means D= the square root of 25 which is 5. This means the distance from the origin to (4,3) is 5 feet. Now the dog can go 10 more feet in the opposite direction of the origin so 5 + 10 (pretty easy math) = 15. The dog can be (at its farthest) 15 feet from the origin. Hope this helps.
-G
