Explanation:
To find the coordinates of the ice cream store, we need to determine its position on the line connecting the grocery store and the restaurant.
First, we find the distance between the grocery store and the restaurant using the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Distance = sqrt((7 - (-5))^2 + (3 - 12)^2)
= sqrt(12^2 + (-9)^2)
= sqrt(144 + 81)
= sqrt(225)
= 15
Next, we calculate 2/3 of the distance from the grocery store to the restaurant:
2/3 * 15 = 10
This means that the ice cream store is located 10 units from the grocery store along the same line.
To find the coordinates of the ice cream store, we start from the grocery store (-5, 12) and move 10 units in the direction towards the restaurant.
The x-coordinate of the ice cream store will be -5 + 10 = 5.
To find the y-coordinate, we calculate the vertical distance between the grocery store and the restaurant:
Vertical distance = 12 - 3 = 9
Since we're moving 10 units along this line, the y-coordinate of the ice cream store will be 12 - 9 = 3.
Therefore, the coordinates of the ice cream store are (5, 3).