RS Aggarwal Solutions for Class 10 Maths Chapter 16 Exercise 16.3: The Physics Wallah academic team has produced a comprehensive answer for Chapter 16: Coordinate Geometry in the RS Aggarwal class 10 textbook. The RS Aggarwal class 10 solution for chapter 16 Coordinate Geometry Exercise-16C is uploaded for reference only; do not copy the solutions.
Before going through the solution of Chapter 16 Coordinate Geometry Exercise-16C, one must have a clear understanding of Chapter 16 Coordinate Geometry. Read the theory of chapter 16 Coordinate Geometry and then try to solve all numerical of exercise-16C. Complete the NCERT exercise questions and utilize them as a guide. You need assistance to get through the Class 10 Math questions in Physics Wallah NCERT solutions. Class 10 Math NCERT solutions were uploaded by Physics Wallah.RS Aggarwal Solutions for Class 10 Maths Chapter 16 Exercise 16.3 PDF
Find the area of △ A B C whose vertices are :
(i) A(1, 2), B (-2, 3) and C(-3, -4) (ii) A (-5,7),B(-4, -5) and C(4,5) (iii) A(3, 8), B(-4, 2) and C(5, -1) (iv) A (10, -6),B (2,5) and C(-1, 3)Find the area of quadrilateral ABCD whose vertices are A(3, -1), B(9, -5), C(14, 0) and D(9, 19).
Find the area of quadrilateral PQRS whose vertices are P(-5, -3), Q(-4,-6), R(2,-3) and S(1,2).
If A(-7, 5), B(-6, -7), C (-3,-8) and D(2,3) are the vertices of a quadrilateral ABCD then find the area of the quadrilateral.
Find the area of △ A B C with A(1, -4) and midpoints of sides through A being (2, -1) and (0, -1)
(i) If the vertices of △ A B C be A(1, -3), B(4, p) and C(-9, 7) and its area is 15 square units, find the values of p.
(ii) The area of a triangle is 5 sq units. Two of its vertices are (2, 1) and (3, -2). If the third vertex is ( 7 2 , y ) , find the value of y.
The are of △ A B C with vertices A(a, 0), O(0, 0) and B(0, b) in square units is
(a) ab (b) 1 2 a b (c) 1 2 a 2 b 2 (d) 1 2 b 2
If P ( a 2 , 4 ) is the midpoint of the line segment joining the points A (-6, 5) and B(-2, 3) then the value of a is
(a) -8 (b) 3 (c) -4 (d) 4
Question
Find the coordinates of point A, where AB is the diameter of a circle whose centre is (2, – 3) and B is (1, 4).
Solution:
Let the coordinates of point A be ( x , y ). Mid-point of AB is (2, – 3), which is the centre of the circle. Coordinate of B = (1, 4) (2, -3) =((x+1)/2 , (y+4)/2) (x+1)/2 = 2 and (y+4)/2 = -3 x + 1 = 4 and y + 4 = -6 x = 3 and y = -10 The coordinates of A(3,-10).If the point A (x, 2) is equidistant from the points B(8, -2) and C(2, -2) find the value of x. Also, find the length of AB.
Question
Determine the ratio in which the line 2x + y – 4 = 0 divides the line segment joining the points A(2, –2) and B(3, 7).
Solution
Consider line 2x + y – 4 = 0 divides line AB joined by the two points A(2, -2) and B(3, 7) in k:1 ratio. Coordinates of point of division can be given as follows: x = (2 + 3k)/(k + 1) and y = (-2 + 7k)/(k + 1) Substituting the values of x and y given equation, i.e. 2x + y – 4 = 0, we have 2{(2 + 3k)/(k + 1)} + {(-2 + 7k)/(k + 1)} – 4 = 0 (4 + 6k)/(k + 1) + (-2 + 7k)/(k + 1) = 4 4 + 6k – 2 + 7k = 4(k+1) -2 + 9k = 0 Or k = 2/9 Hence, the ratio is 2:9.Question
Find the centre of a circle passing through points (6, -6), (3, -7) and (3, 3).
Solution
Let A = (6, -6), B = (3, -7), and C = (3, 3) are the points on a circle. If O is the centre, then OA = OB = OC (radii are equal) If O = (x, y), then OA = √[(x – 6) 2 + (y + 6) 2 ] OB = √[(x – 3) 2 + (y + 7) 2 ] OC = √[(x – 3) 2 + (y – 3) 2 ] Choose: OA = OB, we have After simplifying above, we get -6x = 2y – 14 ….(1) Similarly, OB = OC (x – 3) 2 + (y + 7) 2 = (x – 3) 2 + (y – 3) 2 (y + 7) 2 = (y – 3) 2 y 2 + 14y + 49 = y 2 – 6y + 9 20y =-40 or y = -2 Substituting the value of y in equation (1), we get -6x = 2y – 14 -6x = -4 – 14 = -18 x = 3 Hence, the centre of the circle is located at point (3,-2).Question
Find the ratio in which the line segment joining the points (-3, 10) and (6, – 8) is divided by (-1, 6).
Solution:
Consider the ratio in which the line segment joining (-3, 10) and (6, -8) is divided by point (-1, 6) be k :1. Therefore, -1 = ( 6 k -3)/( k +1) – k – 1 = 6 k -3 7 k = 2 k = 2/7 Therefore, the required ratio is 2: 7.Question
In each of the following, find the value of ‘k’, for which the points are collinear.
(i) (7, -2), (5, 1), (3, -k)
(ii) (8, 1), (k, -4), (2, -5)
Solution:
(i) For collinear points, the area of triangle formed by them is always zero. Let points (7, -2), (5, 1), and (3, k) are vertices of a triangle. Area of triangle = 1/2 [7 { 1- k} + 5(k-(-2)) + 3{(-2) – 1}] = 0 7 – 7k + 5k +10 -9 = 0 -2k + 8 = 0 k = 4 (ii) For collinear points, the area of triangle formed by them is zero. Therefore, for points (8, 1), (k, – 4), and (2, – 5), area = 0 1/2 [8 { -4- (-5)} + k{(-5)-(1)} + 2{1 -(-4)}] = 0 8 – 6k + 10 = 0 6k = 18 k = 3Question
Find the area of the triangle whose vertices are:
(i) (2, 3), (-1, 0), (2, -4)
(ii) (-5, -1), (3, -5), (5, 2)
Solution:
Area of a triangle formula = 1/2 × [x 1 (y 2 – y 3 ) + x 2 (y 3 – y 1 ) + x 3 (y 1 – y 2 )] (i) Here, x 1 = 2, x 2 = -1, x 3 = 2, y 1 = 3, y 2 = 0 and y 3 = -4 Substitute all the values in the above formula, we get Area of triangle = 1/2 [2 {0- (-4)} + (-1) {(-4) – (3)} + 2 (3 – 0)] = 1/2 {8 + 7 + 6} = 21/2 So, the area of the triangle is 21/2 square units. (ii) Here, x 1 = -5, x 2 = 3, x 3 = 5, y 1 = -1, y 2 = -5 and y 3 = 2 Area of the triangle = 1/2 [-5 { (-5)- (2)} + 3(2-(-1)) + 5{-1 – (-5)}] = 1/2{35 + 9 + 20} = 32 Therefore, the area of the triangle is 32 square units.Conceptual Clarity : The solutions provide step-by-step explanations for each problem, helping students understand the fundamental concepts of coordinate geometry such as the distance formula, section formula, and area of triangles.
Enhanced Problem-Solving Skills : By working through various types of problems, students can develop strong problem-solving skills. The solutions illustrate different methods to approach and solve coordinate geometry problems, making students adept at tackling similar questions in exams.
Time Management : With clear and concise solutions, students can learn to solve problems more efficiently, improving their time management skills during exams.
Accuracy : The solutions ensure that students follow the correct procedures and calculations, reducing errors and increasing accuracy in their work.
Confidence Building : Regular practice with accurate solutions builds confidence in students, as they can verify their answers and understand their mistakes, leading to improved performance in tests and exams.