Slope of a Line Connecting Two Points

Q.

A line perpendicular to the line segment joining the points (1, 0) and (2, 3) divides it in the ratio 1 : n. Find the equation of the line.

Q. Point $R(h,k)$ divides a line segment between the axes in the ratio $1:2$. Find equation of the line.

Q.

Find the coordinates of a point which equidistant from the four points $o(0,0,0),A(l,0,0),B(0,m,0)andC(0,0,n)$.

Q.

Match the lines given on the left side with their corresponding slopes on the right..
$\begin{array}{cc}Linepassesthroughthepoints& Slopeoftheline\\ p.\left)\right(1,6\left)and\right(-4,2)& 1.)0\\ q.\left)\right(5,9\left)and\right(2,9)& 2.)-3\\ r.\left)\right(-2,-1\left)and\right(-3,2)& 3.)\frac{4}{5}\\ s.\left)\right(4,0\left)and\right(3,3)& 4.)\frac{5}{3}\end{array}$

1. p - 3 q - 1 r - 2 s - 4

2. p - 3 q - 1 r - 2 s - 2

3. p - 1 q - 3 r - 1 s - 2

4. p - 1 q - 3 r - 2 s - 2

Q. The angle between the $x-$axis and the line joining the points $(3,-1)$ and $(4,-2)$ is

1. ${45}^{\circ }$
2. ${75}^{\circ }$
3. ${120}^{\circ }$
4. ${150}^{\circ }$

Q. The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices (0, 0), (0, 21)and (21, 0) is

1. 133
2. 190
3. 105
4. 233

Q. A line passes through . If slope of the line is m , show that .

Q.

If $z_1,z_2,z_3$ be three complex numbers which are in H.P. And the points $A\left(z_1\right),B\left(z_2\right),C\left(z_3\right)$ are non-collinear, and O is origin, then:

1. O, A, B, C are concyclic

2. O is centroid of ∆ ABC

3. O, A, B, C are collinear

4. None of these

Q. If the coordinates of A and B be (1, 1) and (5, 7), then the equation of the perpendicular bisector of the line segment AB is

1. 2x+3y=18
2. 2x-3y+18=0
3. 2x+3y-1=0
4. 3x-2y+1=0

Q. The area bounded by $y=||x-1|-6|$ and $y=0$ is sq. units

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

Q. The area bounded by $f\left(x\right)=||x-1|-6|$ and $y=0$ is sq. units