Question:
The coordinate of the point dividing internally the line joining the points \( (4,-2) \) and \( (8,6) \) in the ratio \( 7:5 \) is
The coordinate of the point dividing internally the line joining the points \( (4,-2) \) and \( (8,6) \) in the ratio \( 7:5 \) is
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For internal division, weights are proportional to opposite points.
Updated On: May 1, 2026
- \( (16,18) \)
- \( (18,16) \)
- \( \left(\frac{19}{3}, \frac{8}{3}\right) \)
- \( \left(\frac{8}{3}, \frac{19}{3}\right) \)
- \( (7,3) \)
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The Correct Option is C
Solution and Explanation
Concept: Section formula for internal division.
Step 1: Let points be \( A(4,-2), B(8,6) \).
Step 2: Use section formula: \[ \left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right) \]
Step 3: Substitute \( m=7, n=5 \).
\[ x = \frac{7\cdot8 + 5\cdot4}{12} = \frac{56+20}{12} = \frac{76}{12} = \frac{19}{3} \]
Step 4: Compute y-coordinate.
\[ y = \frac{7\cdot6 + 5\cdot(-2)}{12} = \frac{42-10}{12} = \frac{32}{12} = \frac{8}{3} \]
Step 5: Final point: \[ \left(\frac{19}{3}, \frac{8}{3}\right) \]
Step 1: Let points be \( A(4,-2), B(8,6) \).
Step 2: Use section formula: \[ \left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right) \]
Step 3: Substitute \( m=7, n=5 \).
\[ x = \frac{7\cdot8 + 5\cdot4}{12} = \frac{56+20}{12} = \frac{76}{12} = \frac{19}{3} \]
Step 4: Compute y-coordinate.
\[ y = \frac{7\cdot6 + 5\cdot(-2)}{12} = \frac{42-10}{12} = \frac{32}{12} = \frac{8}{3} \]
Step 5: Final point: \[ \left(\frac{19}{3}, \frac{8}{3}\right) \]
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