5. Find a relation between x and y such that the point (x, y) is equidistant from the points (3, 6) and (-3, 4). Here CB is the x-axis and CD is the y-axis. (ii) For collinear points, area of triangle formed by them is zero. 2. Chapter 3 - Pair of Linear Equations in Two Variables. Your email address will not be published. ABCD is a rectangle formed by the points A (-1, – 1), B (-1, 4), C (5, 4) and D (5, -1). Let the points (5, – 2), (6, 4), and (7, – 2) are representing the vertices A, B, and C respectively. However, the diagonals are of different lengths. However, area cannot be negative. • Distance Formula: You will learn how to find the distance between the two points whose coordinates are given. There will be one mark MCQ question, 2mark reasoning questions, and 3 marks short answer questions. Therefore, the coordinates of this point are (8, 20). (ii) Let the points (- 3, 5), (3, 1), (0, 3), and ( – 1, – 4) be representing the vertices A, B, C, and D of the given quadrilateral respectively. Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3). The area of both sides is same. Therefore, AD is the median in ΔABC. Let P(x, y) be the required point. • Section Formula: You will study how to find the coordinates of the point which divides a line segment joining two given points in a given ratio. Can you now find the distance between the two towns A and B discussed in Section 7.2. In each of the following find the value of ‘k’, for which the points are collinear. 3. What is the distance between both the flags? Verify this result for ΔABC whose vertices are A (4, - 6), B (3, - 2) and C (5, 2). Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don't you think ABCD is a square?” Chameli disagrees. Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: (i) (- 1, - 2), (1, 0), (- 1, 2), (- 3, 0), (ii) (- 3, 5), (3, 1), (0, 3), (- 1, - 4), 9. Consider the ratio in which the line segment joining ( -3, 10) and (6, -8) is divided by point ( -1, 6) be k :1. 1. • Introduction: Coordinate geometry is an algebraic tool for studying geometry of figures. 7. Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of ∆ ABC. Its also seen that points A, B and C are collinear. Coordinate Geometry is the branch of Mathematics in which algebraic methods are used to solve geometrical problems is known as coordinate geometry. 7. Therefore, its y-coordinate will be 0. Simplify the above equation and find the value of y. Justify your answer. Let D be the mid-point of side BC of ΔABC. Coordinates of point of division can be given as follows: Substituting the values of x and y given equation, i.e. NCERT Solutions for Class 10 Maths. 1. 4. Point D and Point E divide AB and AC respectively in ratio 1 : 3. Coordinates of Point R will be R (4, 6) OR R (-4, 6). This chapter teaches you the relationship between numerical and geometry and their application in our daily lives. Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle. 2. The solutions provided here are written in simple language with apt information. 4. 5. Therefore, ABCD is a square and hence, Champa was correct. Therefore, the given points are the vertices of a parallelogram. For instance the area of a triangle. The solution has all the exercise questions provided in the NCERT textbook. 2. If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y. Mid-point of AB is (2, – 3), which is the centre of the circle. Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: (i) (- 1, – 2), (1, 0), (- 1, 2), (- 3, 0), (ii) (- 3, 5), (3, 1), (0, 3), (- 1, – 4). Find the coordinates of the points which divide the line segment joining A (- 2, 2) and B (2, 8) into four equal parts. If A and B are (–2, –2) and (2, –4), respectively, find the coordinates of P such that AP = 3. Point P divides the line segment AB in the ratio 3:4. The point at which Rashmi should post her blue flag is the mid- point of the line joining these points. This chapter comes under unit 6 and has a weightage of 6 marks in the board examination. Point Q divides AB internally in the ratio 2:1. y2 = (2×(-3)+1×(-1))/(2+1) = (-6-1)/3 = -7/3, The coordinates of the point Q is (0, -7/3). Distance between points (0, 0) and (36, 15). Distance between these flags can be calculated by using distance formula. Key Features of NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry. Let the vertices of the quadrilateral be A (- 4, – 2), B ( – 3, – 5), C (3, – 2), and D (2, 3). The two opposite vertices of a square are (-1, 2) and (3, 2). Hence, ratio of area of triangle ADE to area of triangle ABC = 1 : 16. Area of ΔABC = 1/2 [(-4) {(-5) – (-2)} + (-3) {(-2) – (-2)} + 3 {(-2) – (-5)}], Area of ΔACD = 1/2 [(-4) {(-2) – (3)} + 3{(3) – (-2)} + 2 {(-2) – (-2)}], Area of quadrilateral ABCD = Area of ΔABC + Area of ΔACD, = (21/2 + 35/2) square units = 28 square units. Join AC and divide quadrilateral into two triangles. Find the distance between the following pairs of points: Distance formula to find the distance between two points (x1, y1) and (x2, y2) is, say d. 2. Let say this point be P(x, y). Now, find the coordinates of the point of division: P (x, y) = ((-4(1)+1)/(1+1) , (5(1)-5)/(1+1)) = (-3/2 , 0). A line is drawn to intersect sides AB and AC at D and E respectively, such that . 1. • Area of the Triangle: You will learn to find the area of the triangle formed by three given points. 3. Find the area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2,-1) taken in order. (v) If A (x1, y1), B (x2, y2) and C (x3, y3) are the vertices of triangle ABC, the coordinates of centroid can be given as follows: 8. Solution: Ex 7.1 Class 10 Maths Question 10. Using distance formula, find which of them is correct. Can you now find the distance between the two towns A and B discussed in Section 7.2. Is the quadrilateral PQRS a square? 6. 7. 10. Also calculate the areas of the triangles in these cases. This chapter has fundamental concepts that lay the foundation for your future studies. Opposite sides of this quadrilateral are of the same length. BYJU’S is India’s top online education provider with the country’s best teachers on its board. 8. Let O (2, 3) be the centre of the circle. To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. If Q (0, 1) is equidistant from P (5, – 3) and R (x, 6), find the values of x. From figure, the coordinates of points A, B, C and D are (3, 4), (6, 7), (9, 4) and (6,1). So, x-axis divides the line segment in the ratio 1:1. 10. Therefore, area of ΔACD is 3 square units. Coordinates of vertices P, Q and R are ( 12, 2) , (13, 6) and (10, 3) respectively. So, the given points can only form 3 sides i.e, a triangle and not a quadrilateral which has 4 sides. These NCERT solutions, prepared by experts at BYJU’S, are a comprehensive study material for the students preparing for the CBSE Class 10 board examination. You have studied in Class IX that a median of a triangle divides it into two triangles of equal areas. 6. The students are to sow the seeds of flowering plants on the remaining area of the plot. Solution: Ex 7.1 Class 10 Maths Question 9. Since two sides of any isosceles triangle are equal. From the figure, it can be observed that points X, Y, Z are dividing the line segment in a ratio 1:3, 1:1, 3:1 respectively. Since the diagonals of a parallelogram bisect each other, the midpoint is same. Verify this result for ΔABC whose vertices are A (4, – 6), B (3, – 2) and C (5, 2). 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in the following figure. Also, find the distances QR and PR. Let the vertices of the triangle be A (4, -6), B (3, -2), and C (5, 2). Find the coordinates of a point A, where AB is the diameter of circle whose centre is (2, – 3) and B is (1,4). If A and B are (-2, -2) and (2, -4), respectively, find the coordinates of P such that AP = 3/7 AB and P lies on the line segment AB. Diagrammatic representations and alternate methods will help you understand the concepts thoroughly. 1. What do you observe? 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