Line Segment Midpoint Dilemma?

📌 CONCEPT: To prove that MB = 2MC, we need to use the concept of mid-point and section formula in the context of line segments.

📐 RULE / FORMULA: According to the section formula, if a point P(x, y) divides a line segment joining the points A(x1, y1) and B(x2, y2) in the ratio m:n, then the coordinates of P are given by ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)). We will use this formula to find the coordinates of M and C.

💡 WORKED EXAMPLE: Let A be (1, 3) and B be (7, 9). Since M is the midpoint of AB, we can find its coordinates using the midpoint formula. Let D divide AB in the ratio 3:4. We can use the section formula to find the coordinates of D. Then, we can find the coordinates of C by taking M as the midpoint of MD. Finally, we can calculate MB and MC to verify that MB = 2MC.

⚠️ COMMON MISTAKE: Students often get confused between the midpoint and section formula, which leads to incorrect calculations. They should carefully apply the correct formula and verify their calculations to avoid this mistake.