Class 10 Exam > Class 10 Notes > Mathematics Class 10 ICSE > Worksheet: Section and Mid-Point Formula
Worksheet: Section and Mid-Point Formula | Mathematics Class 10 ICSE PDF Download
Section A: Very Short Questions
Q1. Find the midpoint of the line joining (2, 5) and (8, -3).
Q2. Find the coordinates of the centroid of triangle with vertices (0, 0), (6, 0), (0, 6).
Q3. Point P(4, 2) is the midpoint of line AB. If A = (6, -1), find B.
Q4. In which ratio does point (7, 2) divide the line joining (5, 6) and (9, 0)?
Q5. Find the point on y-axis equidistant from (2, -3) and (-2, 5).
Section B: Short Answer Questions
Q6. Find the coordinates of the point dividing the line joining (3, -4) and (7, 6) in the ratio 3:1.
Q7. A(-6, 3) and B(6, -1). Find the points of trisection of AB.
Q8. The centroid of triangle is (2, -1). Two vertices are (1, 3) and (3, -5). Find the third vertex.
Q9. Show that the points (2, 3), (4, -1), (6, 3) are collinear using section formula.
Q10. Find the ratio in which the x-axis divides the line joining (2, -4) and (6, 8). Also find the coordinates.
Section C: Long Answer Questions
Q11. Find the coordinates of the centroid of triangle A(2, -2), B(6, 4), C(-4, 2). Verify by showing that centroid divides median in 2:1 ratio.
Q12. Find the points of trisection of the line joining (7, -2) and (-2, 4). Verify that the distance between them is one-third of total length.
Q13. A(1, 2), B(5, -2), C(-3, -4). Find centroid and verify that medians intersect at same point.
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FAQs on Worksheet: Section and Mid-Point Formula - Mathematics Class 10 ICSE
| 1. What is the midpoint formula and how is it derived? |  |
Ans. The midpoint formula is used to find the midpoint between two points in a coordinate plane. If you have two points A(x₁, y₁) and B(x₂, y₂), the midpoint M can be calculated using the formula M = ((x₁ + x₂)/2, (y₁ + y₂)/2). This formula is derived by averaging the x-coordinates and the y-coordinates of the two points.
| 2. How do you apply the section formula in coordinate geometry? | |
Ans. The section formula is used to find a point that divides a line segment into a certain ratio. If point P divides the line segment joining points A(x₁, y₁) and B(x₂, y₂) in the ratio m:n, the coordinates of P can be calculated using the formula P = ((mx₂ + nx₁)/(m+n), (my₂ + ny₁)/(m+n)). This allows us to locate points based on given ratios.
| 3. What are practical applications of the midpoint and section formulas? | |
Ans. Midpoint and section formulas are widely used in various fields such as physics, engineering, and computer graphics. For instance, they can help in determining the center of a line segment in design work, calculating average positions in data analysis, or finding locations in navigation systems.
| 4. Can the midpoint formula be used in three-dimensional space? If yes, how? | |
Ans. Yes, the midpoint formula can be extended to three-dimensional space. If you have two points A(x₁, y₁, z₁) and B(x₂, y₂, z₂), the midpoint M can be found using the formula M = ((x₁ + x₂)/2, (y₁ + y₂)/2, (z₁ + z₂)/2). This gives the average of the coordinates in three dimensions.
| 5. What is the importance of understanding the section formula in coordinate geometry? | |
Ans. Understanding the section formula is crucial in coordinate geometry as it allows for precise calculations of points along lines based on given ratios. This is particularly important in fields such as architecture and computer-aided design, where accurate measurements and placements are essential for effective planning and execution.
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Sep 08, 2025
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