32 solutions available
In a classroom, 4 friends are seated at the points A, B, C and D as shown in the given figure. Champa and Chameli walk into the class and after...
Find a relation between x and y such that the point (x, y) is equidistant from the points (3, 6) and (-3, 4).
Find the distance between the following pairs of points: (i) (2, 3), (4, 1) (ii) (-5, 7), (-1, 3) (iii) (a, b), (-a, -b)
Find the distance between the points (0, 0) and (36, 15).
Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.
Check whether (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.
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)...
Find the point on the x-axis which is equidistant from (2, -5) and (-2, 9).
Find the values of y for which the distance between the points P (2, -3) and Q (10, y) is 10 units.
If Q (0, 1) is equidistant from P (5, -3), and R (x, 6), find the values of x. Also, find the distances QR and PR.
Find the coordinates of the points of trisection of the line segment joining (4, -1) and (-2, -3).
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....
Find the ratio in which line segment joining A (1, -5) and B (-4, 5) is divided by the x-axis. Also, find the coordinates of the point of division.
If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.
Find the coordinates of a point A, where AB is the diameter of a 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 = \(\frac { 3 }{ 7 }\) AB and P lies on the line segment AB.
Find the coordinates of the points which divide the line segment joining A (-2, 2) and B (2, 8) into four equal parts.
Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6).
Find the area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2, -1) taken in order. [Hint: Area of a rhombus = \(\frac { 1 }{ 2 }\)...
Find the area of the quadrilateral whose vertices, taken in order, are (-4, -2), (-3, -5), (3, -2) and (2, 3).
Find the area of the triangle whose vertices are: (i) (2, 3), (-1, 0), (2, -4) (ii) (-5, -1), (3, -5), (5, 2)
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)
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). Find the...
You have studied in Class IX, that a median of a triangle divides it into two triangles of equal areas. Verify this result for ∆ABC whose vertices...
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).
Find a relation between x and y, if the points (x, y), (1, 2) and (7, 0) are collinear.
Find the centre of a circle passing through the points (6, -6), (3, -7) and (3, 3).
The two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of the other two vertices.
The class X students school in krishnagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are...
Let A(4, 2), B(6,5) and C(1, 4) be the vertices of ∆ABC. (i) The median from A meters BC at D. Find the coordinates of the point D. (ii) Find the...
ABCD is a rectangle formed by the points A(-1, -1), B(-1, 4), C(5, 4) and D(5, -1), P, Q, R and S are the mid-points of Ab, BC, CD and DA...
The vertices of a VABC are A(4, 6), B(1, 5) and C(7, 2). A line is drawn to intersect sides AB and AC at D and E respectively. such that \(\frac { AD...
