Coordinate Geometry is a branch of mathematics that deals with the relationship between algebraic equations and geometric shapes on a coordinate plane. It involves plotting points on an x-y axis and using algebraic equations to determine properties of the shapes formed by those points. The basic concepts of coordinate geometry include distance formula, slope formula, and equation of a line. It also involves the study of conic sections, which are shapes that result from intersecting a cone with a plane.
Coordinate Geometry is an important topic for competitive exam students as it tests their ability to understand and apply mathematical concepts in real-world scenarios. Questions on Coordinate Geometry can appear in various competitive exams such as JEE, CAT, GRE, and SAT. These exams require students to solve problems related to finding the distance between two points, slope of a line, equation of a line, intersection of lines, and many other applications of Coordinate Geometry. Understanding the principles of Coordinate Geometry question and answer is also essential for students pursuing careers in fields such as engineering, architecture, and physics.
Example of coordinate geometry MCQ Question & Answer
Suppose there are two points A (3, 4) and B (-2, 5) on a coordinate plane. Find the distance between A and B.
To solve this problem, we use the distance formula, which is:
distance = sqrt[(x2 - x1)^2 + (y2 - y1)^2]
Here, x1 = 3, y1 = 4, x2 = -2, and y2 = 5. Substituting these values in the formula, we get:
distance = sqrt[(-2 - 3)^2 + (5 - 4)^2]
distance = sqrt[(-5)^2 + (1)^2]
distance = sqrt[25 + 1]
distance = sqrt[26]
Therefore, the distance between A and B is sqrt[26] units.
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