NCERT solutions for Mathematics [English] Class 10 chapter 7 - Coordinate Geometry [Latest edition]

Find the distance between the following pairs of points:

(2, 3), (4, 1)

Find the distance between the following pairs of points:

(−5, 7), (−1, 3)

Find the distance between the following pairs of points:

(a, b), (−a, −b)

Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2.

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.

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.

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:

(- 1, - 2), (1, 0), (- 1, 2), (- 3, 0)

Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:

 (−3, 5), (3, 1), (0, 3), (−1, −4)

Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:

(4, 5), (7, 6), (4, 3), (1, 2)

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 distance QR and PR.

Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (−3, 4).

Find the coordinates of the point which divides the join of (–1, 7) and (4, –3) in the ratio 2 : 3.

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. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in the following figure. Niharika runs `1/4` th the distance AD on the 2^nd line and posts a green flag. Preet runs `1/5` th the distance AD on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?

Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6).

Find the ratio in which the 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 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" = 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 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 = `1/2` (product of its diagonals)]