Class 10 Maths - BIHAR
Coordinate Geometry
Coordinate Geometry in Class 10 Bihar Board (BSEB) mathematics builds a bridge between algebra and geometry using the Cartesian plane. This chapter covers locating points, finding distances between two points, dividing line segments in specific ratios, and calculating the area of triangles formed by given coordinates. Mastering this chapter is crucial for BSEB exams as it features regularly in both objective multiple-choice questions and high-scoring subjective questions. It forms the foundational basis for analytical geometry that you will use in higher classes.
Start Learning FreeKey Concepts
Cartesian Coordinate System
A system that uses two perpendicular number lines (X-axis and Y-axis) intersecting at the origin (0,0) to locate any point in a plane using ordered pairs (x, y).
Distance Formula
Used to find the shortest straight-line distance between two points (x1, y1) and (x2, y2) on the Cartesian plane, derived directly from Pythagoras's theorem.
Section Formula
Helps find the coordinates of a point that divides a line segment joining two given points in a specific internal ratio m:n.
Mid-point Formula
A special case of the section formula used to find the exact middle point of a line segment by averaging the X and Y coordinates of its endpoints.
Area of a Triangle
A formula used to calculate the enclosed area of a triangle when the coordinates of its three vertices are given in the Cartesian plane.
Important Formulas
Board Exam Info
In the Bihar (BSEB) Class 10 Mathematics board exam, Coordinate Geometry typically carries around 6 to 10 marks. Questions appear in multiple formats, including 1-mark objective questions, 2-mark short answer questions, and sometimes 5-mark long answer questions involving proofs or multi-step calculations like finding the vertices of quadrilaterals.
Frequently Asked Questions
What is the distance of a point (x, y) from the origin?
The distance of any point (x, y) from the origin (0,0) is given by the simplified formula sqrt(x^2 + y^2).
How do I know if three points are collinear using coordinate geometry?
Three points are collinear if the area of the triangle formed by them is equal to zero, or if the sum of the distances between two pairs equals the distance of the third pair.
Are negative coordinates allowed in the distance formula?
Yes, negative coordinates are very common. When you square the difference of coordinates (e.g., (x2 - x1)^2), the negative sign automatically becomes positive, so it does not affect the final distance.
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