NCERT Maths Solutions Class 11th Chapter 10 Straight Lines Exercise 10.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines prepared by the Mathematics subject experts. All the important topics in Straight Lines are covered in the exerceses and answer comes with a detailed explaanation to help students understand concepts better. These Class Maths NCERT solutions play a crucial role in your preparation for all exams conducted by the CBSE, including the JEE

NCERT Solution for Class 11 Maths Chapter 10 Exercise 10.1

Ex 10.1 Class 11 Maths Question-1

Draw a quadrilateral in the Cartesian plane, whose vertices are (-4, 5),(0, 7), (5, -5) and (-4, -2). Also, find its area.

Ans:

Let ABCD be the given Quadrilateral with vertices A(-4, 5), B(0, 7), C(5, -5) and D(-4, -2).

Then, by plotting A,B,C and D on the Cartesion plane and joing AB,BC,CD and DA the given quadrilateral can br drawn as

Ex 10.1 Class 11 Maths Question-2

The base of an equilateral triangle with side 2a line along they y-axis such that the point of the base is at the origin. Find vertices of the triangle.

Ans:

Let ABC be the given equlateral triangle with side 2a.

Accordingly, AB = BC = CA = 2a

Assume that base BC lies along the y-axis such that the of BC is at the arigin.

i.e, BO = OC = a, where O is the Origin.

Now, it is clear that the coolrdnates of point C are (0, a), while the coordinates of point B are (0, -a).

Noit is clear that line joing a vertex of an equiral tringle with the mid-poing of its opposite side is perpendicular.

Hence, vertex Alies on the y-axis

Ex 10.1 Class 11 Maths Question-3

Find the distance between P(x ₁ Y₁) and Q(x₂,y₂) when ; (i) PQ is parallel to the y-axis,(ii) PQ is parallel to the x- axis.

Ans:

The given points are P(x ₁,y₁) and Q(x₂,y₂).

(i) When PQ is parallel to the y-axis, x ₁ = x₂.

In this case, distance between P and Q=

(ii) When PQ is parallel to the x-axis, y₁ =y₂.

In this case, distance between P and Q =

Ex 10.1 Class 11 Maths Question-4

Find a point on thex-axis, which is equidistant from the point (7,6)and (3,4).

Ans:

Let (a,0) be the point on the x axis that is equidistant from the points (7,6) and (3,4).

Ex 10.1 Class 11 Maths Question-5

Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P(0, -4) and B (8,0).

Ans:

The coordinates of the mid –point of the line segment joining the points P(0, -4) and B(8,0) are

It is known that the slope (m) of a non –vertical line passing through the points (X ₁,Y₁ and (X_{2,Y2) is given by}

Therefore, The required slope of the line passing through (0,0) and (4,-2) is

Hence, the required slope of the line is