English Medium Class 10 - CBSE Important Questions

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).

If the distance between the points (4, p) and (1, 0) is 5, then p is equal to ______.

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

Find the point on the y-axis which is equidistant from the points (S, - 2) and (- 3, 2).

The line segment joining the points A(2, 1) and B (5, - 8) is trisected at the points P and Q such that P is nearer to A. If P also lies on the line given by  2x - y + k= 0  find the value of k.

Find the coordinates of point A, where AB is a diameter of the circle with centre (–2, 2) and B is the point with coordinates (3, 4).

Find the distance between the points (a, b) and (−a, −b).

The points (– 4, 0), (4, 0), (0, 3) are the vertices of a ______.