Important Mathematics Questions of Class X Chapter {Co - Ordinate Geometry} for CBSE Examination 2023
1) If the points (0, 0), (1,2) and (a,b) are collinear, then find the relation between a and b.
2) Find the point which lies on the perpendicular bisector of the line segment joining the points A(-2, -5) and B(2,5).
3) Find the perimeter of a triangle with vertices (0,4), (0,0) and (3,0).
4) AOBC is a rectangle whose three vertices are A(0,3), O(0,0) and B(5,0). What is the length of its diagonal?
5) Find the distance between the points (0,5) and (-5,0).
6) Find the area of a triangle with vertices (a, b+c), (b, c+a) and (c, a+b).
7) If the point P(2,1) lies on the line segment joining the points A(4,2) and B(8,4), then find the relation between AP and AB.
8) Check whether the points (-4, 0), (4,0) and (0,3) are the vertices of an isosceles triangle or equilateral triangle.
9) Find the ratio in which y axis divides the line segment joining the points A(5, -6) and B(-1, -4). Also find the co ordinates of the point of division.
10) Prove that the points (3,0), (6,4) and (-1, 3) are the vertices of a right angle isosceles triangle.
11) The x coordinates of a point P is twice is y coordinate. If P is equidistant from Q(2, -5) and R(-3, 6), find the coordinate of P.
12) Show that circle has its centre at the origin and the point P(5,0) lies on it, the point Q(6,8) lies outside the circle.
13) Show that the points A(-6, 10), B(-4, 6) and C(3, -8) are collinear such that AB = 2/3 AC.
14) Prove that the points (0,0), (5,5) and (-5,5) are the vertices of a right angled isosceles triangle.
15) Prove that the points (0,0), (5,5) and (-5,5) are the vertices of a right angled triangle.
16) Show that triangle ABC with vertices A(-2,0), B(0,2) and C(2,0) is similar to triangle DEF with vertices D(-4,0), E(4,0) and F(0,4).
17) Show that the points A(a, a), B(-a, -a) and C(-a√3, a√3) form an equilateral triangle.
18) If two adjacent vertices of a parallelogram are (3,2) and (-1,0) and the diagonal intersect at (2, -5), Then find the other two vertices.
19) Find the type of triangle formed by points A(-5,6), B(-4,-2, C(7,5).
20) If the points A(1, -2), B(2,3), C(-3, 2) and D(-4, -3) are th vertices of a parallelogram ABCD, then talking AB as the base, find the height of the parallelogram.
21) Find the ratio in which the point (-3, k) divides the line segment joining the points (-5, -4) and (-2, 3). Also find the value of k.
22) If the point (x, y) is equidistant from the points (a+b, b-a) and (a-b, a+b), then prove that bx =ay.
23) Let P and Q be the points of trisection of the line segment joining the points A(2, -2) and B(-7, 4) such that P is nearer to A. Find the coordinates of P and Q.
24) If the points A(0, 2) is equidistant from the points B(3, p) and C (p, 5), find p. Also find the length of AB.
25) If the points A(-2,1), B(a, b) and C (4, -1) are collinear and a-b = 1, find the values of a and b.
26) If the point P(k-1, 2) is equidistant from the points A(3,k) and B(k, 5), find the values of k.
27) Find the ratio in which the line segment joining the point A(3, -3) and B(-2, 7) is divided by x – axis. Also find the coordinates of the point of division.
28) Find the value of k if the points A(k+1, 2k), B(3k, 2k+3) and C5k-1, 5k) are collinear.
29) For the triangle ABC formed by the points A(4, -6), B(3, -2) and C(5,2), verify that median divides the triangle into two triangle of a equal area.
30) Find the ratio in which point P(-1,y) lying on the line segment joining points A(-3, 10) and B(6, -8) divides it. Also find the value of y.
31) Find the point on the x axis which is equidistant from the points (-2,5) and (2, -3).
32) If the points A(2,-4) id equidistant from P(3,8) and Q(-10,y), find the value of y. Also find the distance PQ.
33) Find the coordinates of centre of circle passing through the point (0,0), (-2,1) and (-3,2). Also find its radius.
34) If P(9a-2, -b) divides line segment joining A(3a+1, -3) and B(8a, 5) in the ratio 3 : 1, find the values of a and b. Also determine the value of a2 + b2.
35) Find the points on x – axis which are at a distance of 2√5 form the point (7, -4). How many such points are there?
36) Find the value of x such that PQ = QR where P, Q and Rare the points (2,5), (x, -3) and (7,9) respectively.
37) Find the ratio in which the line 2x + y = 4 divides the join of A(2, -2) and B(3,7). Also find the coordinates of the point of their intersection.
38) Prove that the points (2, -2), (-2, 1) and (5, 2) are the vertices of a right angled triangle. Also find the area of this triangle.
39) If the points C(-1, 2) divides internally the line segment joining the points A(2,5) and B(x, y) in the ratio of 3 : 4, find the value of x2 + y2.40) Check weather (5, - 2) (6, 4) and (7, - 2) are the vertices of an isosceles triangle.
47) Find the values of k so that the area of the triangle with vertices (1, -1), (-4, 2k) and (-k, -5) is 24 sq. units.
48) If A(-4, 8), B(-3, -4), C(0, -5) and D(5,6) are the vertices of a quadrilateral ABCD, find its area.
49) Find the ratio in which the point P(x, 2) divides the line segment joining the points A(12, 5) and B(4, -3). Also find the value of x.
50) If two vertices of an equilateral triangle are (0,0), (3, √3). Find the third vertex.
No comments:
Post a Comment