Question

A hiker is lost in the woods. A search team has created a coordinate grid to represent the woods. Each unit on the grid is one square mile. The hiker was last seen at (5, 10) and could have walked 12 miles in any direction since then. Which equation represents the area the hiker could be in?

A)
(x - 5)2 + (y - 10)2 = 122


B)
(x + 5)2 + (y + 10)2 = 122


C)
(x - 10)2 + (y - 5)2 = 122


D)
(x + 10)2 + (y + 5)2 = 122

Answer 1

The correct answer is A) (x-5)²+(y-10)²=12².

The graph of possible locations would be a circle, since he could be in any direction. 12 would be the radius, since he could be 12 miles away. The center of the circle would be his last location. The equation of a circle is given by:

(x-h)²+(y-k)²=r²

Since (5, 10) is the center and 12 is the radius, this gives us
(x-5)²+(y-10)²=12²