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Q1. What is the coordinates of the point that divides the line segment joining (0, 0) and (6, 8) in the ratio 3:1?
Solution:
Using the section formula: P = ((3*6 + 1*0)/(3+1), (3*8 + 1*0)/(3+1)) = (4.5, 6).
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Q2. What is the coordinates of the midpoint of the line segment joining (3, 7) and (9, 1)?
Solution:
Using the midpoint formula: M = ((3 + 9)/2, (7 + 1)/2) = (6, 4).
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Q3. What is the distance between the points (5, 5) and (5, 9)?
Solution:
Using the distance formula: d = √((5 - 5)² + (9 - 5)²) = √(0 + 16) = √16 = 4.
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Q4. If point C is at (2, 3) and point D is at (10, 7), what is the coordinates of point E that divides CD in the ratio 1:3?
Solution:
Using the section formula: E = ((1*10 + 3*2)/(1+3), (1*7 + 3*3)/(1+3)) = (5, 4).
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