**NCERT
Solutions for Class 11 Maths Chapter 9 ****Straight Lines**** Ex 9.1**

NCERT Solutions for Class 11 Maths Chapter 9 Straight Lines Ex 9.1 are the part of NCERT Solutions for Class 11 Maths. Here you can find
the NCERT Solutions for Class 11 Maths Chapter 9 Straight Lines Ex 9.1.

**Ex 9.1 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.

**Solution:**

The figure of quadrilateral whose vertices are A(-4, 5), B(0, 7), C(5, -5) and D(-4, -2) is given below.

**Ex 9.1 Class 11 Maths Question 2.**

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

**Solution:**

Since base of an equilateral triangle lies along y-axis.

**Ex 9.1 Class 11 Maths Question 3.**

_{1}, y_{1}) and Q(x_{2}, y_{2}) when:**(i)** PQ is parallel to the y-axis,**(ii)** PQ is parallel to the x-axis.

**Solution:**

It is given that the coordinates of P is (x_{1}, y_{1}) and the coordinates of Q is (x_{2}, y_{1}).

The distance between the points P(x_{1}, y_{1}) and Q(x_{2}, y_{2}) is:

**Ex 9.1 Class 11 Maths Question 4.**

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

**Solution:**

Let the point be P(x, y).

Since, the point lies on the x-axis.

∴ y = 0, i.e., the required point is (x, 0).

Since the required point is equidistant from points A(7, 6) and B(3, 4)

⇒ PA = PB

**Ex 9.1 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).

**Solution:**

We are given the two points whose coordinates are P(0, -4) and B(8, 0).

Let A be the midpoint of PB, then

**Ex 9.1 Class 11 Maths Question 6.**

Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (-1, -1) are the vertices of a right angled triangle.

**Solution:**

Let A(4, 4), B(3, 5) and C(-1, -1) be the vertices of ∆ABC.

Let m_{1} and m_{2} be the slopes of AB and AC, respectively.

**Ex 9.1 Class 11 Maths Question 7.**

Find the slope of the line, which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.

**Solution:**

Since the line makes an angle of 30° with the positive direction of y-axis, this line makes an angle of 90° + 30° = 120° with the positive direction of x-axis.

Hence, the slope of the given line, m = tan 120° = –√3

**Ex 9.1 Class 11 Maths Question 8.**

Without using distance formula, show that points (-2, -1), (4, 0), (3, 3) and (-3, 2) are the vertices of a parallelogram.

**Solution:**

Let A(-2, -1), B(4, 0), C(3, 3) and D(-3, 2) be the vertices of the given quadrilateral ABCD. Then,

**Ex 9.1 Class 11 Maths Question 9.**

Find the angle between the x-axis and the line joining the points (3, -1) and (4, -2).

**Solution:**

The given points are A(3, -1) and B(4, -2).

**Ex 9.1 Class 11 Maths Question 10.**

The slope of a line is double of the slope of another line. If tangent of the angle between them is 1/3, find the slopes of the lines.

**Solution:**

Let m_{1} and m_{2} be the slopes of the two lines.

**Ex 9.1 Class 11 Maths Question 11.**

A line passes through (x_{1}, y_{1}) and (h, k). If slope of the line is *m*, show that

k – y_{1} = m (h – x_{1}).

**Solution:**

The given line passes through (x_{1}, y_{1}) and (h, k). Also, the slope of the line is m.

**Related Links:**

**NCERT Solutions for Maths Class 9**