Let AP= PQ = QR = RB = k . Solution: Question 89. y = – 10 x1 + x2 = 2 …..(i) The co-ordinates of mid-points D, E and F are The answers and explanations are given for the practice questions. Also find the area of this triangle. If the points P(-3,9), Q(a, b) and R(4, -5) are collinear and a + b = 1, find the value of a and b. Answer: (c) 5 units Let point P is on Y-axis whose coordinate is (0, y) Question 9. ⇒ 36 + 25 + y2 – 10y = 16 + 9 + y2 – 6y Question 3. Clearly point a is the midpoint of AB. Answer: If the points A(-2,1), B (a, b) and C(4, -1) are collinear and a – b = 1, find the value of a and b. What is the distance between both the flags? Also find the distance PQ. Solution: Question 4. The base BC of an equilateral triangle ABC lies on y-axis. Solution: Question 88. . Find the third vertex of the triangle ABC, if its two vertices are (3,5), (-4, -6) and the coordinates of the centroid are (4, 3). Point P(x, 4) lies on the line segment joining the points A(-5,8) and B(4, -10). ∴ x = 6 and y = 3. Hence P divides AB in ratio 1 : 5. = 4 × \(\frac{37}{2}\) Solution: Question 96. ∴ QP = QR If the point P(x,y) is equidistant from two points A (-3,2) and B (4, -5), prove that y = x- 2. 100 flower pots have been placed at a distance of 1 m from each other along with AD, as shown in figure. ⇒ 10x – 2y = 0 (a) (-7, 0) Solution. Solution: Question 6. (d) None of these. (c) 10 Also find the coordinates of another point D such that BACD is a rhombus. The endpoints of a line segment AB are A(2, 5) and B(1, 9). (a) (5, 5) ⇒ x2 + y2 + 2gx + 2fy + c = 0, If P(2, p) is the mid-point of the line segment joining the points A(6, -5) and B(-2,11), find the value of p. Therefore, the points (-2, -2), (-1, -1), (0, 0), (1, 1) and (2, 2) will satisfy the above condition. As centre is the mid point of AB. Solution: Question 68. Find the values of x and y. If the points (p, q); (m, n) and (p-m,q-n) are collinear, show that pn = qm Solution: Question 19. (b) 6 units B = (cos2 θ, sin2 θ) ⇒ y2 + 6y + 73 = 100 P(x, y) = (11, 15) Prove that the points P(a, b + c), Q(b, c + a) and R(c, a + b) are collinear. Question 11. x2 + y2 + 2gx + 2fy + c = 0, ⇒ 3λ + 3 = 8λ + 2 Find the area of a parallelogram ABCD if three of its vertices are A(2, 4), B(2 + √3,5) and C(2, 6). From (i) and (ii), we get = 8 + 8 = 16 If the coordinates of points A and B are (-2, -2) and (2, – 4) respectively, find the coordinates of P such that AP = 3/7 AB, where P lies on the line segment AB. Let P, Q and R be the points on line segment AB such that ⇒ y = -9 or 3, Question 7. Coordinate Geometry Class 10 Extra Questions Maths Chapter 7 with Solutions Answers October 12, 2020 October 12, 2020 / By Prasanna Here you will find Coordinate Geometry Class 10 Extra Questions Maths Chapter 7 with Answers Solutions, Extra Questions for Class 10 Maths are solved by experts and will guide students in the right direction. For what values of k are the points (8,1), (3, -2k) and (k, -5) collinear? Students who are preparing for their Class 10 exams must go through Important Questions for Class 10 Math Chapter 7 Coordinate Geometry. Area of ∆ABC = 4 × ar (∆DEF) Solution: Question 102. ∴(x + 3)2 + (y + 2)2 = (x + 2)2 + (y – 3)2 at D and E respectively such that AD/AC=AE/AC=1/3. (d) None of these. AB2 + BC2 = (AC)2 …(4) Solution: Question 83. Find the coordinates of P and Q. = x2 + y2 – 6x – 4y + 13 If the area of AABC formed by A(x, y), B(l, 2) and C(2, 1) is 6 square units, then prove that x +y= 15. Then Point M(11,y) lies on the line segment joining the points P(15,5) and Q(9,20). Its distance from the origin is : Let D be the mid-point of hypotenuse AB. If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag? (c) (-4, -4), Question 20. Find the coordinates of point which divide line segment AB joining points A(-2, 2) and B( 2, 8) into four equal parts. If A(-2,3), B(6,5), C(x, – 5) and D(-4, – 3) are the vertices of a quadrilateral ABCD of area 80 sq. Find the value of k, if the points A(8,1), B(3, -4) and C(2, k) are collinear (d) 6 Find the value of k if P(4, -2) is the mid point of the line segment joining the points A(5k, 3) and B(-k, —7). Solution: Question 80. ... Find the coordinate of the point which will divide the line joining the point (2,4) and (7,9) internally in the ratio 1:2? Find the coordinates of the points which divide the line segment joining A(-2, 2) and B(2, 8) into four equal parts. (a) 10 units units, find the value(s) of p. ⇒ -1 + x = 12; – 1 + y = 9 points P, Q, R and S divide the line segment joining the points A(l, 2) and B(6, 7) in 5 equal parts. (c) 17 units, Question 14. Find a point P on they-axis which is equidistant from the points A(4,8) and B(- 6, 6). POPULAR PAGES. Solution. The distance between points (7, 3) and (-5, -2) is : Let points P(a, a), Q(-a, -a) and R(-a√3, a√3) are given, then ⇒ y(y + 9) – 3 (y + 9) = 0 Solution: Question 38. Question 10. (a) 18 units Solution: Question 23. Verify this result for ∆ABC whose vertices are A (4, -6), B (3, – 2) and C (5, 2). The distance between the points (2, 0) and (-1, 4) is : If A and B are (-2, -2) and (2, -4), respectively, find the coordinates of P such that If the area of ∆ABC formed by A(x, y), B(1, 2) and C(2, 1) is 6 square units, then prove x + y = 15. The x-coordinate of a point P is twice its y-coordinate. ∴ AP = BP ⇒ AP2 = BP2 The centre of a circle is (2a, a – 7). Solution: Question 116. ⇒ x2 – 4x + 4 + 25 = x2 + 4x + 4 + 81 Solution: Question 117. (iii) The given condition is x = y. Let the point A(-1, 6) divide the line joining B(-3, 10) and C(6, -8) in the ratio k : 1. Class 10 Maths MCQs for Coordinate Geometry. Question 5. (a) 5 units. ⇒ (x – 2)2 + (0 + 5)2 = (x + 2)2 + (0 – 9)2 For x-axis : Since, ABCD is a parallelogram. Question 20. The mid-points of the sides of a triangle are (1, 2), (0, -1) and (2, -1). Answer: The third vertex of an equilateral triangle whose other two vertices are (1, 1) and (1, -1) respectively is : ∵ OA = OB Find the value of£, for which the points A(6, -1), B(& – 6) and C(0, -7) are collinear. y2 + y3 = -2 …..(v) Let the coordinates of a point are (x, y). (b) 2nd quadrant Solution. Since, the position of towns A and B are given (0, 0) and (36, 15), respectively and so, the distance between them is 39 km. 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