The straight line $2x - 3y + 17 = 0$ is perpendicular to the line passing through the points $(7, 17)$ and $(15, \beta)$. Then,$\beta$ equals:

If the slope of a line passing through the point $A(3, 2)$ is $3/4$,then the points on the line which are $5$ units away from $A$ are:

Find the equation of the line perpendicular to the line $2x - 3y = 5$ and passing through the point $(1, -1)$.

If two vertical poles of heights $20\,m$ and $80\,m$ stand apart on a horizontal plane,then the height (in $m$) of the point of intersection of the lines joining the top of each pole to the foot of the other is:

In an isosceles triangle $ABC$,the coordinates of the points $B$ and $C$ on the base $BC$ are respectively $(1, 2)$ and $(2, 1)$. If the equation of the line $AB$ is $y = 2x$,then the equation of the line $AC$ is

If a straight line through the point $P(1, 2)$,which makes an angle $45^{\circ}$ with the $X$-axis,meets the line $3x + 4y + 5 = 0$ at $Q$,then the length of $PQ$ equals ......... units.