Which of the following points has a distance of 10 from the point (-1,2)?
A.(10,2)
B.(-1,-12)
C.(-1,10)
D.(-11,2)
The distance between two points (x1, y1) and (x2, y2) in a coordinate plane can be found using the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Using the distance formula, we can calculate the distance between (-1, 2) and each of the given points:
A. Distance = √((10 - (-1))^2 + (2 - 2)^2) = √(11^2 + 0^2) = √(121 + 0) = √121 = 11
B. Distance = √((-1 - (-1))^2 + (-12 - 2)^2) = √(0^2 + (-14)^2) = √(0 + 196) = √196 = 14
C. Distance = √((-1 - (-1))^2 + (10 - 2)^2) = √(0^2 + 8^2) = √(0 + 64) = √64 = 8
D. Distance = √((-11 - (-1))^2 + (2 - 2)^2) = √((-10)^2 + 0^2) = √(100 + 0) = √100 = 10
The point that has a distance of 10 from the point (-1, 2) is option D, (-11, 2).