Common Mistakes Made in ICSE Class 10 Board Exams Chapter Section and Midpoint Formula

Chapter Overview

Section formula is used to find the coordinates of a point which divides the line segment joining two given points in a given ratio.

If point P divides the line segment joining the points A(x₁, y₁) and B(x₂, y₂), then the coordinates of point P are given by



The mid-Point formula is used to find the coordinates of the mid-point of the line segment joining two given points.

Let P(x, y) be a point lying on a line segment AB, where the coordinates of A and B are (x₁, y₁) and (x₂, y₂) respectively. Suppose P divides AB in the ratio 1: 1. In other words, P is the mid-point of AB.
⟹ AP = PB
The coordinates of P are given by



The Centroid of the triangle is the point which divides all the three medians of a triangle in the ratio 2:1.

If AD is a median of ΔABC and G is its centroid, then 

If the vertices of ΔABC are A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃).

Then the coordinate of the centroid is given by 



Common Mistakes

Application of Formulas:

There is some confusion amongst students while applying the section formula.

The following image clearly illustrates the correct way to apply the section formula.




Also, some students get confused with the formula of the centroid of a Triangle.

The coordinate of the centroid is given by


Basic calculation errors
Basic calculation errors were observed among several candidates, like multiplication, addition and division errors.
Some students forget to divide the sum in the numerator by the denominator.

Representing the coordinates incorrectly
The coordinates of points were written without opening and closing brackets. The correct and only way of writing points for coordinates is in the form (x, y).
Example:
Show (2,3) instead of 2,3.

Examples for Practice:

1. The line segment joining the points M (5, 7) and N (-3, 2) is intersected by the y-axis at point L. Write down the abscissa of L. Hence, find the ratio in which L divides MN. Also, find the coordinates of L.
   Solution: Click here
   
2. Find the ratio in which the line joining (-2, 5) and (-5, -6) is divided by the line y = -3. Hence find the point of intersection.
   Solution: Click here
3. Find the coordinates of points of trisection of the line segment joining points A(2, -2) and B(-7, 4).
   Solution: Click here
4. The coordinates of point A, where AB is the diameter of a circle whose recentre is (2,3) and B is (1,4)?
   (a) (3,-10)
   (b) (-3,10)
   (c) (1,-10)
   (d) (3,2)
   Solution: Click here

Conclusion

In short, to ace the chapter on Section and Mid-Point Formula, one should practice more examples of different types, this will help them to have a firm grip on calculations and also help them to remember the formulas easily.

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