Final answer:
To find the location that is 2/3 the distance from point D to point S, first find the distance between D and S using the distance formula. Multiply the distance by 2/3 to find 2/3 of the distance. Subtract that value from the x-coordinate of D to find the location.
Step-by-step explanation:
To find the location that is 2/3 the distance from point D to point S, we first need to find the distance between D and S. The distance between two points can be found using the distance formula, which is √((x2 - x1)^2 + (y2 - y1)^2) in the Cartesian coordinate system. In this case, the coordinates of D are (-12, 0) and the coordinates of S are (3, 0). Plugging these values into the distance formula, we get: √((3 - (-12))^2 + (0 - 0)^2) = √(15^2 + 0) = √225 = 15.
Next, we need to find 2/3 of the distance between D and S. To do this, we multiply the distance by 2/3: (2/3) * 15 = 10.
Finally, to find the location that is 2/3 the distance from D to S, we start from D and move 10 units towards S. Since we are moving towards S, we subtract 10 from the x-coordinate of D: -12 - 10 = -22.