The coordinates of point B are (0.4, 7.2).
Here's how to find the coordinates of point B:
1. Weighting based on the ratio: We're given that B divides CA in a 3:2 ratio. This means the distance between B and C is 3/5 of the total distance CA, and the distance between B and A is 2/5 of CA.
2. Calculating the vector from C to A: Represent the vector pointing from C to A as CA = A-C. This vector captures the direction and magnitude of the line segment CA.
3. Finding B's coordinates: Since B is 3/5 of the way from C to A, its coordinates can be found by adding 3/5 times the CA vector to C's coordinates. Mathematically, B = C + (3/5) * CA.
4. Plugging in the values: Substitute C = (4, 6) and CA = (-2, 8) - (4, 6) = (-6, 2) into the formula. B = (4, 6) + (3/5) * (-6, 2) = (0.4, 7.2).
Therefore, the coordinates of point B are (0.4, 7.2).
Question:
Given the coordinates of points C and A as C(4, 6) and A(-2, 8) respectively, determine the coordinates of point B that divides the line segment CA into a ratio of 3:2.