What is the distance between these two locations?

Question

(12, 2)
(2, -4)

Answer 1

The distance between these two points can be calculated using the distance formula in 2D space:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the coordinates:
Distance = sqrt((2 - 12)^2 + (-4 - 2)^2)
Distance = sqrt((-10)^2 + (-6)^2)
Distance = sqrt(100 + 36)
Distance = sqrt(136)
Distance ≈ 11.66

Therefore, the distance between the points (12, 2) and (2, -4) is approximately 11.66 units.

Answer 2

Which of the following points has a distance of 11 from the point (-7,4)?(1 point)
Responses

(-7, -1)
(-7, -1)

(4, 4)
(4, 4)

(10, 4)
(10, 4)

(-10, 4)

Answer 3

To find which of the given points has a distance of 11 from the point (-7,4), we can calculate the distance between each point and (-7,4) using the distance formula and see which one is equal to 11.

Let's calculate the distances:
1. Distance from (-7,4) to (-7, -1):
Distance = sqrt((-7 - (-7))^2 + (-1 - 4)^2)
Distance = sqrt(0 + 25)
Distance = sqrt(25) = 5

2. Distance from (-7,4) to (4, 4):
Distance = sqrt((4 - (-7))^2 + (4 - 4)^2)
Distance = sqrt(11^2 + 0)
Distance = sqrt(121) = 11

3. Distance from (-7,4) to (10, 4):
Distance = sqrt((10 - (-7))^2 + (4 - 4)^2)
Distance = sqrt(17^2 + 0)
Distance = sqrt(289) = 17

4. Distance from (-7,4) to (-10, 4):
Distance = sqrt((-10 - (-7))^2 + (4 - 4)^2)
Distance = sqrt((-3)^2 + 0)
Distance = sqrt(9) = 3

Therefore, the point that has a distance of 11 from the point (-7,4) is (4,4).