PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions

Find the slope of a line passing through the following point:

 (−3, 2) and (1, 4)

Find the slope of a line passing through the following point:

\[(a t_1^2 , 2 a t_1 ) \text { and } (a t_2^2 , 2 a t_2 )\]

Find the slope of a line passing through the following point:

(3, −5), and (1, 2)

State whether the two lines in each of the following are parallel, perpendicular or neither.

Through (5, 6) and (2, 3); through (9, −2) and (6, −5)

State whether the two lines in each of the following are parallel, perpendicular or neither.

Through (9, 5) and (−1, 1); through (3, −5) and (8, −3)

State whether the two lines in each of the following is parallel, perpendicular or neither.

Through (6, 3) and (1, 1); through (−2, 5) and (2, −5)

State whether the two lines in each of the following is parallel, perpendicular or neither.

Through (3, 15) and (16, 6); through (−5, 3) and (8, 2).

Find the slope of a line (i) which bisects the first quadrant angle (ii) which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.

Using the method of slope, show that the following points are collinear A (4, 8), B (5, 12), C (9, 28).

Using the method of slope, show that the following points are collinear A (16, − 18), B (3, −6), C (−10, 6) .

What is the value of y so that the line through (3, y)  and (2, 7) is parallel to the line through (−1, 4) and (0, 6)?

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.