Which of the following points has a distance of 10 from the point (−1, 2) ?(1 point)
Responses
(10, 2)
Left Parenthesis 10 comma 2 Right Parenthesis
(−1, 10)
Left Parenthesis negative 1 comma 10 Right Parenthesis
(−11, 2)
Left Parenthesis negative 11 comma 2 Right Parenthesis
(−1, −12)
To find the distance between two points, we can use the distance formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Let's calculate the distance between (-1, 2) and each of the given points:
1) Distance between (-1, 2) and (10, 2):
Distance = √[(10 - (-1))^2 + (2 - 2)^2]
= √[(11)^2 + (0)^2]
= √[121 + 0]
= √121
= 11
2) Distance between (-1, 2) and (-1, 10):
Distance = √[(-1 - (-1))^2 + (10 - 2)^2]
= √[(0)^2 + (8)^2]
= √[0 + 64]
= √64
= 8
3) Distance between (-1, 2) and (-11, 2):
Distance = √[(-11 - (-1))^2 + (2 - 2)^2]
= √[(-10)^2 + (0)^2]
= √[100 + 0]
= √100
= 10
4) Distance between (-1, 2) and (-1, -12):
Distance = √[(-1 - (-1))^2 + (-12 - 2)^2]
= √[(0)^2 + (-14)^2]
= √[0 + 196]
= √196
= 14
So, the point that has a distance of 10 from (-1, 2) is (−11, 2).