Lines Parallel and Perpendicular to a Given Line

Show that the perpendicular bisectors of the sides of a triangle are concurrent.

Find the coordinates of the foot of the perpendicular from the point $(-1,3)$ to the line $3x-4y-16=0$.

Find the image of the point $(3,8)$ with respect to the line $x+3y=7$ assuming the line to be a plane mirror.

The line through $(h,3)$ and $(4,1)$ intersects the line $7x-9y-19=0$ at right angle. Find the value of $h$.

Find the equation of the right bisector of the line segment joining the points $(3,4)$ and $(-1,2)$.

The perpendicular from the origin to the line $y=m x+c$ meets it at the point $\left(-1,2\right)$. Find the values of $m$ and $c$.

Find the equation of a line drawn perpendicular to the line $\frac{x}{4}+\frac{y}{6}=1$ through the point where it meets the $y-$axis.

Find the equation to the straight line parallel to $3x-4y+6=0$ and passing through the middle point of the join of points $(2,3)$ and $(4,-1)$.

If the image of the point $(2,1)$ with respect to the line mirror be $(5,2)$, find the equation of the mirror.

Find the image of the point $(2,1)$ with respect to the line mirror $x+y-5=0$.

Find the equation of the right bisector of the line segment joining the points $(a,b)$ and $\left(a_1,b_1\right)$.

Find the equation of the straight line which has $y-$intercept equal to $\frac{4}{3}$ and is perpendicular to $3x-4y+11=0$.

Find the equation of the straight line perpendicular to $5x-2y=8$ and which passes through the mid-point of the line segment joining $(2,3)$ and $(4,5)$.

Find the equation of the straight line perpendicular to $2x-3y=5$ and cutting off an intercept $1$ on the positive direction of the $x-$axis.

Find the equation of the straight line through the point $(\alpha ,\beta )$ and perpendicular to the line $lx+my+n=0$.

If the image of the point $(2,1)$ with respect to a line mirror is $(5,2)$, find the equation of the mirror.

Find the equations of the altitudes of a $\Delta ABC$ whose vertices are $A(1,4), B(-3,2)$ and $C(-5,-3)$.

Find the equation of the perpendicular bisector of the line joining the points $(1,3)$ and $(3,1)$.

Find the equation of a line passing through $(3,-2)$ and perpendicular to the line $x-3y+5=0$.

Find the projection of the point $(1,0)$ on the line joining the points $(-1,2)$ and $(5,4)$.