English Medium कक्षा १० - CBSE Important Questions for Mathematics

If the point P(x, y) is equidistant from the points A(a + b, b – a) and B(a – b, a + b). Prove that bx = ay.

If the point P(2, 2) is equidistant from the points A(−2, k) and B(−2k, −3), find k. Also find the length of AP.

In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. 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.

Using distance formula, find which of them is correct.

Two vertices of an isosceles triangle are (2, 0) and (2, 5). Find the third vertex if the length of the equal sides is 3.

Find the points on the x-axis, each of which is at a distance of 10 units from the point A(11, –8).

Point A lies on the line segment PQ joining P(6, -6) and Q(-4, -1) in such a way that `(PA)/( PQ)=2/5` . If that point A also lies on the line 3x + k( y + 1 ) = 0, find the value of k.

Points P, Q, R and S divide the line segment joining the points A(1,2) and B(6,7) in five equal parts. Find the coordinates of the points P,Q and R

The base BC of an equilateral triangle ABC lies on y-axis. The coordinates of point C are (0, −3). The origin is the midpoint of the base. Find the coordinates of the points A and B. Also, find the coordinates of another point D such that ABCD is a rhombus.

The midpoint P of the line segment joining points A(-10, 4) and B(-2, 0) lies on the line segment joining the points C(-9, -4) and D(-4, y). Find the ratio in which P divides CD. Also, find the value of y.

Find the coordinates of the points of trisection of the line segment joining the points (3, –2) and (–3, –4) ?

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 ?

For what values of k are the points (8, 1), (3, –2k) and (k, –5) collinear ?

The long and short hands of a clock are 6 cm and 4 cm long respectively. Find the sum of the distances travelled by their tips in 24 hours. (Use π = 3.14) ?

Show that the points (−2, 3), (8, 3) and (6, 7) are the vertices of a right triangle ?

If `P(a/2,4)`is the mid-point of the line-segment joining the points A (−6, 5) and B(−2, 3), then the value of a is

If A and B are the points (−6, 7) and (−1, −5) respectively, then the distance

2AB is equal to

Find the value of y for which the distance between the points A (3, −1) and B (11, y) is 10 units.

Point P(x, 4) lies on the line segment joining the points A(−5, 8) and B(4, −10). Find the ratio in which point P divides the line segment AB. Also find the value of x.

Find the area of the quadrilateral ABCD, whose vertices are A(−3, −1), B (−2, −4), C(4, − 1) and D (3, 4).

The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is ______.