Commerce (English Medium) कक्षा ११ - CBSE Question Bank Solutions

What can be said regarding a line if its slope is  zero ?

What can be said regarding a line if its slope is positive ?

What can be said regarding a line if its slope is negative?

Show that the line joining (2, −3) and (−5, 1) is parallel to the line joining (7, −1) and (0, 3).

Show that the line joining (2, −5) and (−2, 5) is perpendicular to the line joining (6, 3) and (1, 1).

Without using Pythagoras theorem, show that the points A (0, 4), B (1, 2) and C (3, 3) are the vertices of a right angled triangle.

If three points A (h, 0), P (a, b) and B (0, k) lie on a line, show that: \[\frac{a}{h} + \frac{b}{k} = 1\].

The slope of a line is double of the slope of another line. If tangents of the angle between them is \[\frac{1}{3}\],find the slopes of the other line.

Consider the following population and year graph:
Find the slope of the line AB and using it, find what will be the population in the year 2010.

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

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

Line through the points (−2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x. 

Find the value of x for which the points (x, −1), (2, 1) and (4, 5) are collinear.

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

By using the concept of slope, show that the points (−2, −1), (4, 0), (3, 3) and (−3, 2) are the vertices of a parallelogram.

A quadrilateral has vertices (4, 1), (1, 7), (−6, 0) and (−1, −9). Show that the mid-points of the sides of this quadrilateral form a parallelogram.

Find the equation of a straight line with slope 2 and y-intercept 3 .

Find the equation of a straight line  with slope − 1/3 and y-intercept − 4.

Find the equation of a straight line with slope −2 and intersecting the x-axis at a distance of 3 units to the left of origin.