Match the items in Column A with Column B using the table below.
| Column A | Column B |
|---|---|
The coordinates of the points P and Q on the line \(x + 5y = 13\) which are at a distance of 2 units from the line \(12x - 5y + 26 = 0\) | (3, 1), (-7, 11) |
The coordinates of the point on the line \(x + y = 4\), which are at a unit distance from the line \(4x + 3y - 10 = 0\) | \(\left(\dfrac{1}{3}, \dfrac{11}{3}\right), \left(\dfrac{4}{3}, \dfrac{7}{3}\right)\) |
The coordinates of the point on the line joining A(-2,5) and B(3,1) such that AP = PQ = QB | \(\left(1, \dfrac{12}{5}\right), \left(-3, \dfrac{16}{5}\right)\) |
| Column A | Matched Item from Column B |
|---|---|
The coordinates of the points P and Q on the line \(x + 5y = 13\) which are at a distance of 2 units from the line \(12x - 5y + 26 = 0\) | \(\left(1, \dfrac{12}{5}\right), \left(-3, \dfrac{16}{5}\right)\) |
The coordinates of the point on the line \(x + y = 4\), which are at a unit distance from the line \(4x + 3y - 10 = 0\) | (3, 1), (-7, 11) |
The coordinates of the point on the line joining A(-2,5) and B(3,1) such that AP = PQ = QB | \(\left(\dfrac{1}{3}, \dfrac{11}{3}\right), \left(\dfrac{4}{3}, \dfrac{7}{3}\right)\) |
Match the items in Column A with Column B using the table below.
| Column A | Column B |
|---|---|
Parallel to y-axis | \(\lambda = -\dfrac{3}{4}\) |
Perpendicular to \(7x + y - 4 = 0\) | \(\lambda = \dfrac{1}{3}\) |
Passes through (1,2) | \(\lambda = \dfrac{17}{41}\) |
Parallel to x-axis | \(\lambda = 3\) |
| Column A | Matched Item from Column B |
|---|---|
Parallel to y-axis | \(\lambda = 3\) |
Perpendicular to \(7x + y - 4 = 0\) | \(\lambda = -\dfrac{3}{4}\) |
Passes through (1,2) | \(\lambda = \dfrac{1}{3}\) |
Parallel to x-axis | \(\lambda = \dfrac{17}{41}\) |
Match the items in Column A with Column B using the table below.
| Column A | Column B |
|---|---|
Through the point (2,1) | 2x - y = 4 |
Perpendicular to the line \(x + 2y + 1 = 0\) | x + y - 5 = 0 |
Parallel to the line \(3x - 4y + 5 = 0\) | x - y - 1 = 0 |
Equally inclined to the axes | 3x - 4y - 1 = 0 |
| Column A | Matched Item from Column B |
|---|---|
Through the point (2,1) | x - y - 1 = 0 |
Perpendicular to the line \(x + 2y + 1 = 0\) | 2x - y = 4 |
Parallel to the line \(3x - 4y + 5 = 0\) | 3x - 4y - 1 = 0 |
Equally inclined to the axes | x + y - 5 = 0 |