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ICSE Class X Notes 2021 : (Indian Education Society IES Orion, Mumbai)

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Rutvij Dangi
Indian Education Society IES Orion, Mumbai

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Co-ordinate Geometry 01. Introduction & Distance formula 02. Section formula and Mid- point formula 03. Equation of line 04. Doubts + Menti Q5. Given a line ABCD in which AB = BC = CD, B = (0, 3) and C = (1, 8). Find the coordinates of A and D. Q5. Given a line ABCD in which AB = BC = CD, B = (0, 3) and C = (1, 8). Find the coordinates of A and D. Co-ordinate Geometry 01. Introduction & Distance formula 02. Section formula and Mid- point formula 03. Equation of line 04. Doubts + Menti Equation of line Slope of a Line = It is the angle made by the line w.r.t. positive direction of x-axis in Anti clock-wise direction Slope Y B (x2,y2) m = tan y2 y1 m Slope = x x 2 1 O A (x1,y1) X Equation of coordinate axes 1) Equation of x axis, y = 0 2) Equation of y axis, x = 0 y (0, 3) (0, 1) ( 3, 0) ( 1, 0) O (1, 0) (3, 0) (0, 1) (0, 3) x=0 x y=0 Equation of coordinate axes 1) Equation of x axis, y = 0 2) Equation of y axis, x = 0 y (0, 3) (0, 1) ( 3, 0) ( 1, 0) O (1, 0) (3, 0) (0, 1) (0, 3) x=0 x y=0 Q. Find the equation of a line if Parallel to y axis at a distance of 5 units to the left side of it. Solution : 5 units Y-axis As required line is to the left of Y axis, hence a is negative. Equation of line parallel to x axis, at a distance of b units y = b. Equation of line parallel to y axis, at a distance of a units x = a. The equation of line is x = 5 (0,0) X-axis Slope point form Consider a line passing through point A(x1,y1) & having slope m Suppose any arbitrary point P(x, y) on this line Slope of AP = y y1 x x1 = m (given) Equation of line is given by y y1 = m (x x1) P(x, y) m A (x1,y1) Two point form Consider a line passing through two points A(x1,y1) &B (x2,y2) Slope of AP = Slope of AB = y y1 As A, P and B lies on x x1 same line y2 y1 x2 x1 Again let arbitrary point P(x, y) on the line mAP = mAB Equation of line is given by = y y1 x x1 A (x1,y1) P(x, y) y2 y1 = x x 2 1 B (x2,y2) Slope intercept form Consider a line having slope = m and y-intercept = c Now use slope-point form y y1 = m (x x1) y c = m(x 0) y = mx + c m P(0, c) c O X Slope intercept form Consider a line having slope = m and y-intercept = c Now use slope-point form y c = m(x 0) m P(0, c) c O X y y1 = m (x x1) y = mx + c Q1. Find the inclination of a line whose gradient is (i) 1 (ii) (iii) Q1. Find the inclination of a line whose gradient is (i) 1 (ii) (iii) Solution : Q2. Find the equation of a straight line parallel to y - axis and passing through the point (-3, 5). Solution : Q3. The equation of the line PQ is 3y - 3x + 7 = 0 (i) Write down the slope of the line PQ. (ii) Calculate the angle that the line PQ makes with the positive direction of x - axis. Solution : Q4. Find the equation of the line passing through the point (2, -5) and making intercept of -3 on the y -axis. Q4. Find the equation of the line passing through the point (2, -5) and making intercept of -3 on the y -axis. Solution : Q5. Find the equation of the line passing through the points P(5, 1) and Q(1, -1). Hence, show that the points P, Q and R (11, 4) are collinear. Q5. Find the equation of the line passing through the points P(5, 1) and Q(1, -1). Hence, show that the points P, Q and R (11, 4) are collinear. Solution : Q6. Find the equation of the line that has x-intercept = -3 and is perpendicular to 3x + 5y = 1. Q6. Find the equation of the line that has x-intercept = -3 and is perpendicular to 3x + 5y = 1. Solution : Q7. The ordinate of a point lying on the line joining the points (6, 4) and (7, -5) is -23. Find the co-ordinates of that point. Q7. The ordinate of a point lying on the line joining the points (6, 4) and (7, -5) is -23. Find the co-ordinates of that point. Solution : Menti Q1. The slope of a line which makes an angle of 30o with the positive direction of x - axis is A B C D 1 Solution : Q1. The slope of a line which makes an angle of 30o with the positive direction of x - axis is A B C D 1 Q2. The inclination of the line A 30o B 60o C 45o D 0o Solution : Q2. The inclination of the line A 30o B 60o C 45o D 0o Q3. If the lines 2x + 3y = 5 and kx 6y =7 are parallel, then the value of k is A 4 B -4 C D Solution : Q3. If the lines 2x + 3y = 5 and kx 6y =7 are parallel, then the value of k is A 4 B -4 C D Q4. In ABC, A(3, 5), B(7, 8) and C(1, -10). Find the equation of the median through A. A x + 6y = 23 B 2x + y = 14 C 6x + y = 23 D 6x - y = 14 Q4. In ABC, A(3, 5), B(7, 8) and C(1, -10). Find the equation of the median through A. Q4. In ABC, A(3, 5), B(7, 8) and C(1, -10). Find the equation of the median through A. Solution : Q4. In ABC, A(3, 5), B(7, 8) and C(1, -10). Find the equation of the median through A. A x + 6y = 23 B 2x + y = 14 C 6x + y = 23 D 6x - y = 14 Q5. Find the equation of a straight line whose inclination is 60o and which passes through the point (0, -3). A 3x - y - 3 =0 B x - y - 3 =0 C x - 3y - 2=0 D None of these Q5. Find the equation of a straight line whose inclination is 60o and which passes through the point (0, -3). Solution : Q5. Find the equation of a straight line whose inclination is 60o and which passes through the point (0, -3). A 3x - y - 3 =0 B x - y - 3 =0 C x - 3y - 2=0 D None of these GPPRO LIVE Interactive classes: LIVE Classes by India s Best Master Teachers Personalized Attention in class. Full recordings of all classes along with notes, assignments, tests, and more. Complete Curriculum Structured Long term batch insync with your curriculum All Chapterwise - Micro courses to cover one chapter at a time At least 2 Live classes for each chapter every month Complete Crash Course before exams to revise entire syllabus Freedom to make your own study plan and curriculum Test Series Assignments Learning Material Regular Performance Reports Reach out to me @ gopal.paliwal@vedantu.com

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