English Medium इयत्ता १० - CBSE Important Questions for Mathematics

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 ______.

1. Make a labelled figure on the basis of the given information and calculate the distance of the boat from the foot of the observation tower.
2. After 10 minutes, the guard observed that the boat was approaching the tower and its distance from tower is reduced by 240(`sqrt(3)` - 1) m. He immediately raised the alarm. What was the new angle of depression of the boat from the top of the observation tower?

In which ratio the y-axis divides the line segment joining the points (5, – 6) and (–1, – 4)?

Assertion (A): The ratio in which the line segment joining (2, -3) and (5, 6) internally divided by x-axis is 1:2.

Reason (R): as formula for the internal division is `((mx_2 + nx_1)/(m + n) , (my_2 + ny_1)/(m + n))`

Based on the above information answer the following questions using the coordinate geometry.

1. Find the distance between Lucknow (L) to Bhuj (B).
2. If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
3. Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P)
   [OR]
   Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).

If the vertices of a parallelogram PQRS taken in order are P(3, 4), Q(–2, 3) and R(–3, –2), then the coordinates of its fourth vertex S are ______.

Statement A (Assertion): If the coordinates of the mid-points of the sides AB and AC of ∆ABC are D(3, 5) and E(–3, –3) respectively, then BC = 20 units.

Statement R (Reason): The line joining the mid-points of two sides of a triangle is parallel to the third side and equal to half of it.

A tiling or tessellation of a flat surface is the covering of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. Historically, tessellations were used in ancient Rome and in Islamic art. You may find tessellation patterns on floors, walls, paintings etc. Shown below is a tiled floor in the archaeological Museum of Seville, made using squares, triangles and hexagons.

A craftsman thought of making a floor pattern after being inspired by the above design. To ensure accuracy in his work, he made the pattern on the Cartesian plane. He used regular octagons, squares and triangles for his floor tessellation pattern

Use the above figure to answer the questions that follow:

1. What is the length of the line segment joining points B and F?
2. The centre ‘Z’ of the figure will be the point of intersection of the diagonals of quadrilateral WXOP. Then what are the coordinates of Z?
3. What are the coordinates of the point on y-axis equidistant from A and G?
   OR
   What is the area of Trapezium AFGH?

The distance of the point (–4, 3) from y-axis is ______.

The coordinates of the point where the line 2y = 4x + 5 crosses x-axis is ______.