Section Formula
ICSE · Class 10 · Mathematics
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Find the coordinates of point P that divides the line segment joining A(2, 3) and B(8, 9) internally in the ratio 1:2.
What is the midpoint of the line segment joining points M(4, 6) and N(10, 2)?
Find the centroid of triangle with vertices A(0, 0), B(6, 0), and C(3, 9).
Point P(5, 7) divides the line segment joining A(3, 4) and B(x, y) in the ratio 2:3. Find the coordinates of B.
Sample Questions
Which of the following ratios can be used in the section formula? (Select all correct answers)
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2:3, 1:1, 4:7, 3:2
For internal division, both parts of the ratio must be positive. Ratios like 5:0 or 0:3 are invalid because they would place the point at one of the endpoints, not between them.
The coordinates of the midpoint of line segment joining (a, b) and (c, d) are:
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((a+c)/2, (b+d)/2)
The midpoint formula states that for points (x₁, y₁) and (x₂, y₂), the midpoint is ((x₁+x₂)/2, (y₁+y₂)/2). Here x₁=a, y₁=b, x₂=c, y₂=d.
If the centroid of a triangle is at (4, 5) and two vertices are at (2, 3) and (6, 7), find the third vertex.
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(4, 5)
Let third vertex be (x, y). Using centroid formula: 4 = (2+6+x)/3 → 12 = 8+x → x = 4. Similarly, 5 = (3+7+y)/3 → 15 = 10+y → y = 5. Therefore third vertex = (4, 5).
Point P divides line segment AB in ratio 3:4. If A = (1, 2) and B = (8, 9), what is the x-coordinate of P?
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4
Using section formula for x-coordinate: x = (m×x₂ + n×x₁)/(m+n) = (3×8 + 4×1)/(3+4) = (24+4)/7 = 28/7 = 4.
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