Final answer:
To find the coordinate of location B, we can use the concept of section formula in coordinate geometry. Given that location A is at (-1, -4) and location C is at (-3, -8), and the ratio AC:CB = 2:1, the coordinates of B can be calculated as (-5/3, -16/3).
Step-by-step explanation:
To find the coordinate of location B, we can use the concept of section formula in coordinate geometry. The section formula states that if a point C divides the line segment AB in the ratio m:n, then the coordinates of C can be found using the following formula:
xC = (m * xB + n * xA) / (m + n)
yC = (m * yB + n * yA) / (m + n)
Given that location A is at (-1, -4) and location C is at (-3, -8), and the ratio AC:CB = 2:1, we can substitute these values into the formula to find the coordinates of B.
Let's calculate the coordinates of location B:
xB = (1 * (-3) + 2 * (-1)) / (1 + 2) = (-3 - 2) / 3 = -5/3
yB = (1 * (-8) + 2 * (-4)) / (1 + 2) = (-8 - 8) / 3 = -16/3
Therefore, the coordinate of location B is (-5/3, -16/3).
Without all the specific values for the two scenarios provided by the student, we can use the method outlined above to find the coordinates of B in both cases. Since each scenario has different coordinates for A and C and different ratios for AC:CB, the calculations for B's coordinates will differ. However, the methodology and geometric principles relevant to both problems remain consistent - they are applications of the Section Formula in a division of a line segment in a given ratio.