If the line passing through $(4, 3)$ and $(2, k)$ is perpendicular to the line $y = 2x + 3$,then the value of $k$ is:

Consider the following population and year graph (Fig.),find the slope of the line $AB$ and using it,find what will be the population in the year $2010$?

The equation of the line,where the length of the perpendicular segment from the origin to the line is $4$ and the inclination of this perpendicular segment with the positive direction of the $X$-axis is $30^{\circ}$,is:

Find the general equation of a line perpendicular to $x + y + 4 = 0$ and passing through the point $(1, 2)$.

The points on the straight line $3x - 4y + 1 = 0$ which are at a distance of $5$ units from the point $(3, 2)$ are

Let $u = \hat{i} - 2\hat{j}$ and $v = -3\hat{i} + 5\hat{j}$. Consider three points $P, Q,$ and $R$ having position vectors $-\frac{1}{7}\hat{i}$,$-\frac{1}{4}\hat{j}$,and $-2\hat{i} + 3\hat{j}$ respectively. Among these,the points on the line segment passing through $u$ and $v$ are