Скачать или смотреть Internal and external division of ratios

*CORE CONCEPT:*
Internal and external division of ratios involves calculating the coordinates of a point that divides a line segment based on a specified ratio.

*TOPICS COVERED:*
When to use internal division to find coordinates of a point on a segment.
When to use external division for points outside the segment.
How to apply internal and external division in practical problems (B1 level).

*EXAMPLE SENTENCES:*
Example 1: Divide the segment AB in the ratio 1:2. If A is at (0, 0) and B is at (3, 3), the point that divides AB internally is P = (1, 1).
Example 2: Divide the segment AB in the ratio 3:2. If A is at (2, 1) and B is at (8, 5), the point that divides AB externally is P = (22, 13).
Example 3: Divide the segment AB in the ratio 5:4. If A is at (1, 2) and B is at (6, 8), the point that divides AB internally is P = (4.33, 6.33).

*GRAMMAR RULES:*
Identify coordinates of endpoints (A and B) and the ratio → Use the internal division formula for internal division.
Use the external division formula for external division → Calculate coordinates using the same points and ratio.

*COMMON ERRORS:*
Wrong: Using the wrong formula for external division instead of internal division. → Right: Use the internal division formula correctly by ensuring to sum the ratio parts.
Wrong: Forgetting to sum the parts of the ratio in the formula. → Right: Double-check the coordinates of points A and B before applying the formula.
Wrong: Incorrectly identifying the coordinates of points A and B. → Right: Use the external division formula only when required, ensuring correct subtraction.

*STUDENT QUESTIONS:*
How do I find the coordinates of a point that divides a segment?
When to use the internal division formula?
Is my calculation for external division correct?
What's the difference between internal and external division?
How do I apply division of ratios in practical problems?

*KEY CONCEPTS:*
Division of ratios, internal division, external division, coordinates, B1 level, geometry.