NCERT SOLUTIONS FOR CLASS 10 MATHS COORDINATE GEOMETRY CHAPTER 7 EX 7.1

Question 1.
Find the distance between the following pairs of points:
(i) (2, 3), (4, 1)
(ii) (-5, 7), (-1, 3)
(iii) (a, b), (-a, -b)
Solution:

Ex 7.1 Class 10 Maths Question 2.
Find the distance between the points (0, 0) and (36, 15).
Solution:

Ex 7.1 Class 10 Maths Question 3.
Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.
Solution:

Ex 7.1 Class 10 Maths Question 4.
Check whether (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.
Solution:

Ex 7.1 Class 10 Maths Question 5.
In a classroom, 4 friends are seated at the points A, B, C and D as shown in the given 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.

Solution:

Ex 7.1 Class 10 Maths Question 6.
Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer.
(i) (-1, -2), (1, 0), (-1, 2), (-3, 0)
(ii) (-3, 5), (3, 1), (0, 3), (-1, -4)
(iii) (4, 5), (7, 6), (4, 3), (1, 2)
Solution:

Ex 7.1 Class 10 Maths Question 7.
Find the point on the x-axis which is equidistant from (2, -5) and (-2, 9).
Solution:

Ex 7.1 Class 10 Maths Question 8.
Find the values of y for which the distance between the points P (2, -3) and Q (10, y) is 10 units.
Solution:

Ex 7.1 Class 10 Maths Question 9.
If Q (0, 1) is equidistant from P (5, -3), and R (x, 6), find the values of x. Also, find the distances QR and PR.
Solution:

Ex 7.1 Class 10 Maths Question 10.
Find a relation between x and y such that the point (x, y) is equidistant from the points (3, 6) and (-3, 4).
Solution:

Class 10 Maths Coordinate Geometry Mind Maths

Coordinate of a Point in XY – Plane

The Perpendicular distance of x a point from the y-axis is called its x-coordinate or abscissa. The perpendicular distance y of a point from the x-axis is called its y-coordinate or ordinate. The x and y taken together in order is called coordinte of point denoted by (x, y).
The coordinate of the points on x-axis are of the form (x, 0) and the points on the y-axis are of the form(0, y). Coordinate of origin is (0, 0).

Sign-conventions in the XY-Plane

The x and y-axis divide the plane into four parts known as quadrants denoted by I, II, III and IV. The sign of x and y-coordinates in each of the quadrant is shown below:

Distance Formula

The distance between any two points
P(x₁, y₁) and Q(x₂, y₂) in the plane is given by,

Also the distance of the point P(x₁, y₁) from the origin is

Section Formula

The coordinates of the point P(x, y) which divides the line segment joining the points A(x₁, y₁) and B(x₂, y₂) internally in the ratio m₁ : m₂ i.e., PAPB=m1m2

The coordinates of the point P(x, y) which divides the line segment joining the points A(x₁, y₁) and B(x₂, y₂) externally in the ratio, m₁ : m₂ i.e., PAPB=m1m2 are

(iii) If the ratio in which P divides AB is K : 1, then the coordinates of the point P will be

Mid-Point Formula

The coordinates of the mid point P of the line segment joining the points A(x₁, y₁) and B(x₂, y₂) is

Area of a Triangle

The area of ∆ABC formed by the vertices A(x₁, y₁), B(x₂, y₂) is given by

Note:
(i) Area of triangle = 12 × base × Altitude
(ii) Area of polygon can be calculated by dividing it into the triangular region.
(iii) If three points are collinear then area of the triangle formed by them is zero.