10 Question MCQ (including Assertion)

The line through \((2,3)\) and \((k,7)\) is parallel to \(2x-y+5=0\). The value of \(k\) is

The equation of the line parallel to the \(y\)-axis and passing through \((-2,3)\) is

Assertion: The roads represented by \(y=2x+3\) and \(y=2x-5\) are parallel.
Reason: The perpendicular distance between the roads is \(\dfrac{8}{\sqrt5}\) units.

Assertion (A): The line passing through \( (2, 3) \) and \( (4, 5) \) is perpendicular to the line passing through \( (3, 4) \) and \( (5, 2) \).

Reason (R): Two non-vertical lines are perpendicular to each other if and only if the product of their slopes is \( 1 \) (i.e., \( m_1 m_2 = 1 \)).

The distance between the parallel lines \(3x-4y+7=0\) and \(3x-4y+5=0\) is

The perpendicular distance of the point \((3,-5)\) from the line \(3x-4y-26=0\) is

A line passes through \((2,2)\) and cuts positive intercepts on the coordinate axes whose sum is \(9\). The possible equations of the line are

Assertion (A): The image of the point \( (1, 2) \) in the line \( x = 0 \) is \( (-1, 2) \).

Reason (R): If a line acts as a plane mirror for a point, the line is the perpendicular bisector of the line segment joining the point and its image.

A sensor is to be placed on the \(x\)-axis so that it is equidistant from the stations \((7,6)\) and \((3,4)\). The sensor should be placed at