Math Problem Statement
Line segment is drawn between points A(2,-4,3) and B(6,8,-5). A. Find point that divides the segment in the ratio 4:3. B,if point P is shifted by (1,-2,3) determine new co ordinates of P
Solution
Part A: Find the point that divides the segment in the ratio 4:3
The formula to find the coordinates of the point dividing a line segment joining points and in the ratio is:
Here, , , , and .
Calculation of :
So, the point dividing the segment in the ratio 4:3 is:
Part B: Shift by
If is shifted by , the new coordinates are calculated as:
Calculation of new coordinates:
The new coordinates of are:
Final Answer:
A. The point dividing the segment in the ratio is:
B. After shifting by , the new coordinates are:
Do you want a step-by-step breakdown of any part?
Expanding Questions:
- How do you determine the ratio when dividing a segment between points in space?
- What happens if the segment is divided externally instead of internally?
- How can the same formula be extended to higher dimensions (e.g., 4D or 5D)?
- What is the significance of the shift vector in coordinate transformations?
- How do different ratios affect the position of the dividing point?
Tip:
Always simplify the ratio into its lowest terms before applying the section formula to avoid unnecessary
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Ratios
Vector Shifts
Formulas
Section formula: P(x, y, z) = [(mx2 + nx1)/(m+n), (my2 + ny1)/(m+n), (mz2 + nz1)/(m+n)]
Vector shift: P'(x', y', z') = (x + dx, y + dy, z + dz)
Theorems
Section formula theorem for dividing a line segment in a given ratio
Suitable Grade Level
Grades 9-11
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