Coordinate geometry:
The chapter 'Coordinate geometry' is a completely scorbale chapter and it covers six marks in board exam. It covers the concepts like distance formula and section formula.
Most possible variation of question types that we can expect in board exam as per previous year question paper are discussed below.
| Total marks - 6 | |
| Variation 1 | Variation 2 |
Total marks = 6
|
Total marks = 6
|
To prepare well for the board examination, it is necessary to understand the following concepts clearly.
- Distance formula - find the distance between two points.
- Section formula - find point of intersection, ratio of dividing line segment.
| Important Concept (Learning Outcomes) | Expected Question Type | Concept dealt with |
| Distance formula - to find distance between two points | Sec A, Sec B | Distance between two points |
| Distance formula - to find the vertices of polygons | Sec C , Sec D | Vertices of triangle |
| Section formula - to find the ratio of dividing the line segment, to find the point of dividing the line segment | Sec B, Sec D | Point of dividing line segment Ratio of dividing line segment |
| Section formula - Trisection, dividing line segment into four parts | Sec D, Sec E | Trisection |
Let us recall the concepts in Real Numbers:
| NAME | FORMULAS |
| DISTANCE FORMULA | \(d = \sqrt{(x_{2}-x_{1})^2+ (y_{2}-y_{1})^2}\) |
| MIDPOINT | \((x,y) = (\frac{x_{2}+x_{1}}{2},\frac{y_{2}+y_{1}}{2})\) |
| SECTION FORMULA | \((x,y) = (\frac{mx_{2}+nx_{1}}{m+n},\frac{my_{2}+ny_{1}}{m+n})\) |
| CENTORID | \((x,y) = (\frac{x_{3}+x_{2}+x_{1}}{3},\frac{y_{3}+y_{2}+y_{1}}{3})\) |
Common mistakes to avoid:
1. Sign and coordinate errors: Interchanging the \(x-\) and \(y-\) coordinates, missing negative signs, or incorrectly representing points on the axes. Remember: a point on the \(x-axis\) is \((x,0)\), while a point on the \(y-axis\) is \((0,y)\).
2. Errors in the distance formula: Failing to square the differences, forgetting the square root in the final step, or incorrectly assigning \((x_1, y_1)\) and \((x_2, y_2)\) to the given points.
3. Errors in the section formula: Interchanging the given ratio \(m:n\), applying the midpoint formula when a specific ratio is given, handling signs incorrectly in external division, or mixing up the \(x-\) and \(y-\)coordinates.
4. Errors in Finding the Area of a Triangle: Forgetting to take the absolute value of the calculated expression, which may result in a negative area, and failing to verify collinearity when required.
5. Incomplete geometry proof: Declaring a figure a square or rectangle just by checking side lengths. You must also check diagonals as well.
Exam tips & tricks:
1. For \((x, y)\), distance from the origion is given by \(\sqrt{x^2 + y^2}\)
2. Axis shortcut: Distance from \(x\)-axis \(=|y|\), from \(y-\)axis \(=|x|\)
3. Equidistance shortcut: If \(PA = PB\), use \(PA^2 = PB^2\) to avoid square roots.
4. Midpoint: in parallelograms, rectangle, rhombus and squares use equal diagonal's midpoints to find the missing vertices.
5. use area \(=0\) for quick collinearity check.
6. Don't use midpoint formula when ratio is given.
7. Don't conclude collinearity from only \(2\) distances checks.
8. \(k:1\) Ratio Trick: Assume the ratio as \(k:1\) to reduce variables.