English Medium इयत्ता १० - CBSE Question Bank Solutions for Mathematics

The coordinates of the point P are (−3, 2). Find the coordinates of the point Q which lies on the line joining P and origin such that OP = OQ.

Which point on the y-axis is equidistant from (2, 3)  and (−4, 1)?

The three vertices of a parallelogram are (3, 4) (3, 8) and (9, 8). Find the fourth vertex.

Find the centre of the circle passing through (5, -8), (2, -9) and (2, 1).

Find the value of k, if the point P (0, 2) is equidistant from (3, k) and (k, 5).

If two opposite vertices of a square are (5, 4) and (1, −6), find the coordinates of its remaining two vertices.

Show that the points (−3, 2), (−5,−5), (2, −3) and (4, 4) are the vertices of a rhombus. Find the area of this rhombus.

If G be the centroid of a triangle ABC, prove that:

AB² + BC² + CA² = 3 (GA² + GB² + GC²)

If (−2, 3), (4, −3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates of its centroid.

In Fig. 14.36, a right triangle BOA is given C is the mid-point of the hypotenuse AB. Show that it is equidistant from the vertices O, A  and B. 

We have a right angled triangle,`triangle BOA`  right angled at O. Co-ordinates are B (0,2b); A (2a, 0) and C (0, 0).

Find the coordinates of the circumcentre of the triangle whose vertices are (3, 0), (-1, -6) and (4, -1). Also, find its circumradius.

Find a point on the x-axis which is equidistant from the points (7, 6) and (−3, 4).

A (3, 2) and B (−2, 1)  are two vertices of a triangle ABC whose centroid G has the coordinates `(5/3,-1/3)`Find the coordinates of the third vertex C of the triangle.

Show that the points A(5, 6), B(1, 5), C(2, 1) and D(6,2) are the vertices of a square.

Find the point on x-axis which is equidistant from the points (−2, 5) and (2,−3).

Find the value of x such that PQ = QR where the coordinates of P, Q and R are (6, -1), (1, 3) and (x, 8) respectively.

Prove that the points (0, 0), (5, 5) and (-5, 5) are the vertices of a right isosceles triangle.

Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:

A(-1,-2) B(1, 0), C (-1, 2), D(-3, 0)

Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:

A(-3, 5) B(3, 1), C (0, 3), D(-1, -4)