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Find the coordinates of the point that divides the segment joining (1, 2) and (3

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Question: Find the coordinates of the point that divides the segment joining (1, 2) and (3, 4) in the ratio 1:3.

Options:

  1. (2, 3)
  2. (1.5, 2.5)
  3. (2.5, 3.5)
  4. (3, 4)

Correct Answer: (2.5, 3.5)

Solution: 

Using the section formula: (mx2 + nx1)/(m+n), (my2 + ny1)/(m+n) = (1*3 + 3*1)/(1+3), (1*4 + 3*2)/(1+3) = (3 + 3)/4, (4 + 6)/4 = (6/4, 10/4) = (1.5, 2.5).

Find the coordinates of the point that divides the segment joining (1, 2) and (3

Practice Questions

Q1
Find the coordinates of the point that divides the segment joining (1, 2) and (3, 4) in the ratio 1:3.
  1. (2, 3)
  2. (1.5, 2.5)
  3. (2.5, 3.5)
  4. (3, 4)

Questions & Step-by-Step Solutions

Find the coordinates of the point that divides the segment joining (1, 2) and (3, 4) in the ratio 1:3.
  • Step 1: Identify the coordinates of the two points. The first point is (1, 2) and the second point is (3, 4).
  • Step 2: Identify the ratio in which the segment is divided. The ratio is 1:3.
  • Step 3: Assign values to m and n based on the ratio. Here, m = 1 and n = 3.
  • Step 4: Use the section formula to find the x-coordinate of the dividing point. The formula is (mx2 + nx1) / (m + n).
  • Step 5: Substitute the values into the formula for the x-coordinate: (1*3 + 3*1) / (1 + 3).
  • Step 6: Calculate the x-coordinate: (3 + 3) / 4 = 6 / 4 = 1.5.
  • Step 7: Use the section formula to find the y-coordinate of the dividing point. The formula is (my2 + ny1) / (m + n).
  • Step 8: Substitute the values into the formula for the y-coordinate: (1*4 + 3*2) / (1 + 3).
  • Step 9: Calculate the y-coordinate: (4 + 6) / 4 = 10 / 4 = 2.5.
  • Step 10: Combine the x and y coordinates to get the final answer: (1.5, 2.5).
  • Section Formula – The section formula is used to find the coordinates of a point that divides a line segment in a given ratio.
  • Ratios – Understanding how to apply ratios correctly in the context of dividing a segment.
  • Coordinate Geometry – Application of coordinate geometry principles to solve problems involving points in a plane.
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