Boards Concepts Booster Class 10 Coordinate Geometry

1. BOARDS CONCEPTS BOOSTER COORDINATE GEOMETRY  Download Doubtnut Today Ques No. Question CONCEPT FOR BOARDS || Chapter COORDINATE GEOMETRY 1. INTRODUCTION 1 1. What is co-ordinate geometry ?  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter COORDINATE GEOMETRY 1. INTRODUCTION 2 2. Regular coordinate axes  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter COORDINATE GEOMETRY 1. INTRODUCTION 3 3. Cartesian coordinate of a point  Click to LEARN this concept/topic on Doubtnut

2. CONCEPT FOR BOARDS || Chapter COORDINATE GEOMETRY 1. INTRODUCTION 4 4. Quadrant  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter COORDINATE GEOMETRY 1. INTRODUCTION 5 5. Some Important points  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter COORDINATE GEOMETRY 2. DISTANCE B/W TWO POINTS 1. Theorem: The distance between two points sqrt((x_2-x_1)^2+(y_2-y_1)^2) and is given by 6 P(x1;y1) Q(x2;y2)  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter COORDINATE GEOMETRY 2. DISTANCE B/W TWO POINTS 2. If the point (x;y) is equidistant from the points prove that bx = ay and 7 (a + b;b − a) (a − b; a + b)  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter COORDINATE GEOMETRY 2. DISTANCE B/W TWO POINTS 8 3. Some Useful Points

3.  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter COORDINATE GEOMETRY 3. SECTION FORMULA 1. The coordinates of the point which divides the line segment joining the points and internally in the ratio m:n are given by (x1;y1) (x2; y2) mx2+ nx1 (x = ; y 9 m + n my2+ ny1 ) = m + n  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter COORDINATE GEOMETRY 3. SECTION FORMULA 2. (i) Find the coordinates of the point which divides the line segment joining the points (6;3) and (-4;5) in the ratio 3:2 internally 10  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter COORDINATE GEOMETRY 3. SECTION FORMULA 3. (iv) The three vertices of a parallelogram are taken in order (-1;0); (3;1) and (2;2) respectively. Find the coordinates of 4th vertex. 11  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter COORDINATE GEOMETRY 3. SECTION FORMULA

4. 12 4. (ii)In what ratio does the x axis divide the line segment joining the points . Find the coordinate of a point of intersection (2; − 3) and (5;6)  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter COORDINATE GEOMETRY 3. SECTION FORMULA 5. (iii)Prove that the points (-2;-1) ; (1;0);(4;3) and (1;2) are the vertices of the parallelogram . Is this a rectangle ? 13  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter COORDINATE GEOMETRY 4. SOME APPLICATIONS OF SECTION FORMULA 1. Theorem: Prove that the coordinates of centroid of the triangle whose coordinates are (x1;y1); (x2; y2) and (x3;y3) are 14 x1+ x2+ x3 ( ; 3 y1+ y2+ y3 ) 3  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter COORDINATE GEOMETRY 4. SOME APPLICATIONS OF SECTION FORMULA 2. If the coordinates of the midpoints of the sides of a triangle are (1;1);(2;-3) and (3;4). Find its centroid. 15  Click to LEARN this concept/topic on Doubtnut

5. CONCEPT FOR BOARDS || Chapter COORDINATE GEOMETRY 5. AREA OF TRIANGLE 1. Theorem : The area of a triangle the coordinates of whose vertices are (x1;y1); (x2; y2) and 16 (x3;y3) is 1/2|(x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|`  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter COORDINATE GEOMETRY 5. AREA OF TRIANGLE 17 2. Find the Area of polygon  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter COORDINATE GEOMETRY 5. AREA OF TRIANGLE 18 3. Find area of triangle formed by the points A(5;2);B(4;7) and C (7;-4)  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter COORDINATE GEOMETRY 5. AREA OF TRIANGLE 4. Find area of quadrileteral ABCD whose vertices are respectively A(1; 1); B(7; − 3); 19 C(12;2) and D(7;21)`  Click to LEARN this concept/topic on Doubtnut

6. CONCEPT FOR BOARDS || Chapter COORDINATE GEOMETRY 5. AREA OF TRIANGLE 5. Prove that (a; b + c); 20 (b;a + c); (c; a + b) are collinear.  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter COORDINATE GEOMETRY 5. AREA OF TRIANGLE 21 6. For what value of x will the points (x;-1);(2;1) and (4;5) lie on a line ?  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter COORDINATE GEOMETRY 5. AREA OF TRIANGLE 7. If the vertices of a triangle having integral coordinates . Prove that triangle can't be equileteral . 22  Click to LEARN this concept/topic on Doubtnut  Download Doubtnut to Ask Any Math Question By just a click  Get A Video Solution For Free in Seconds  Doubtnut Has More Than 1 Lakh Video Solutions  Free Video Solutions of NCERT, RD Sharma, RS Aggarwal, Cengage (G.Tewani), Resonance DPP, Allen, Bansal, FIITJEE, Akash, Narayana, VidyaMandir  Download Doubtnut Today