ACT Math · Coordinate geometry

Two cell towers are located at coordinates (0,0) and (9,12), measured in miles. What is the distance between the two towers?

Two cell towers are located at coordinates (0,0)(0,0) and (9,12)(9,12), measured in miles. What is the distance between the two towers?

Answer and explanation

Answer: G: 15 miles

Use the distance formula: d=(9−0)2+(12−0)2=81+144=225=15d=\sqrt{(9-0)^2+(12-0)^2}=\sqrt{81+144}=\sqrt{225}=15 miles, choice G. This is a 99-1212-1515 right triangle, which is a 33-44-55 triangle scaled by 33. Choice J (225225) stops before taking the square root. Choice H (2121) adds the horizontal and vertical distances, which would be the distance traveled along the grid, not the straight line. Choice F (10.510.5) is half of 2121. The straight-line distance must be less than 2121 and greater than 1212.

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