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

## 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 2a 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.

Find the distance between P(x1, y1) and Q(x2, y2) 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 (x1, y1) and the coordinates of Q is (x2, y1).
The distance between the points P(x1, y1) and Q(x2, y2) 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 m1 and m2 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 m1 and m2 be the slopes of the two lines.

### Ex 9.1 Class 11 Maths Question 11.

A line passes through (x1, y1) and (h, k). If slope of the line is m, show that

k – y1 = m (h – x1).

Solution:
The given line passes through (x1, y1) and (h, k). Also, the slope of the line is m.