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, −12)
Left Parenthesis negative 1 comma negative 12 Right Parenthesis
(−11, 2)
Left Parenthesis negative 11 comma 2 Right Parenthesis
(−1, 10)
Left Parenthesis negative 1 comma 10 Right Parenthesis
To find the distance between two points, we can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) represents the coordinates of the first point and (x2, y2) represents the coordinates of the second point.
In this case, the first point is (-1, 2) and we are looking for a point that has a distance of 10 from this point. Let's calculate the distances for each of the given points:
1. (10, 2):
d = sqrt((10 - (-1))^2 + (2 - 2)^2) = sqrt((11)^2 + (0)^2) = sqrt(121 + 0) = sqrt(121) = 11
The distance is 11, not 10.
2. (-1, -12):
d = sqrt(((-1) - (-1))^2 + ((-12) - 2)^2) = sqrt((0)^2 + (-14)^2) = sqrt(0 + 196) = sqrt(196) = 14
The distance is 14, not 10.
3. (-11, 2):
d = sqrt(((-11) - (-1))^2 + (2 - 2)^2) = sqrt((-10)^2 + (0)^2) = sqrt(100 + 0) = sqrt(100) = 10
The distance is 10, which is what we're looking for.
4. (-1, 10):
d = sqrt(((-1) - (-1))^2 + (10 - 2)^2) = sqrt((0)^2 + (8)^2) = sqrt(0 + 64) = sqrt(64) = 8
The distance is 8, not 10.
Therefore, the point (-11, 2) is the one that has a distance of 10 from the point (-1, 2).