Ratio in Which Line Divides Segment Joining 2 Points

Q.

The line segment joining the points $(-3,-4)$ and $(1,-2)$ is divided by y-axis in the ratio

1. 1 : 3

2. 3 : 1

3. 3 : 2

4. 2 : 3

Q.

The ratio in which the line $3x+4y+2=0$ divides the distance between $3x+4y+5=0$and $3x+4y-5=0$, is

1. $7:3$

2. $3:7$

3. $2:3$

4. None of these

Q. A rod of length $l$ moves such that its ends $A$ and $B$ always lie on the lines $3x-y+5=0$ and $y+5=0$ respectively. Then the locus of the point $P$ which divides $AB$ internally in the ratio of $2:1,$ is

1. $l^2=\frac{1}{4}(3x+3y-5{)}^2+(3y+15{)}^2$
2. $l^2=\frac{1}{4}(3x-3y-5{)}^2+(3y-5{)}^2$
3. $l^2=\frac{1}{4}(3x-3y+5{)}^2+(3y-5{)}^2$
4. $l^2=\frac{1}{4}(3x-3y-5{)}^2+(3y+15{)}^2$

Q. If $A=(-2,3,4),B=(1,2,3)$ are two points and P is the point of intersection of $AB$ and $zx-$ plane then $P_x+P_y+P_z=$

Q.

The line segment joining the points $(1,2)$ and $(-2,1)$ is divided by the line $3x+4y=7$ in the ratio

1. 3 : 4

2. 4 : 3

3. 9 : 4

4. 4 : 9

Q. The ratio in which the line $3x+2y=2$ divides the line joining the points $(-6,-2)$ and $(4,3)$ is

1. $3:2$ internally
2. $2:3$ externally
3. $3:2$ externally
4. $3:1$ internally

Q. The ratio in which the line $3x+2y=2$ divides the line joining the points $(-6,-2)$ and $(4,3)$ is

1. $3:1$ internally
2. $3:2$ internally
3. $2:3$ externally
4. $3:2$ externally

Q. The straight line $2x–3y=1$ divides the circular region $x^2+y^2\le 6$ into two parts. If $S=\{(2,\frac{3}{4}),(\frac{5}{2},\frac{3}{4}),(\frac{1}{4},-\frac{1}{4}),(\frac{1}{8},\frac{1}{4})\},$ then the number of point(s) in S lying inside the smaller part is

Q.

The equation of the straight line which passes through the point $(-4,3)$ such that the portion of the line between the axes is divided internally by the point in the ratio 5 : 3 is

1. none of these

2. $9x-20y+96=0$

3. $9x+20y=24$

4. $20x+9y+53=0$

Q. The line segment joining the points $(3,5)$ and $(-4,2)$ is divided by $y$-axis in the ratio:

1. $5:3$
2. $3:5$
3. $4:3$
4. $3:4$

Q.

Find the ratio in which the line $3x+4y+2=0$ divides the distance between the lines $3x+4y+5=0$ and $3x+4y-5=0$.

Q.

The ratio in which the line $3x+4y+2=0$ divides the distance between the lines $3x+4y=0$ and $3x+4y-5=0$ is

1. 2 : 5

2. 1 : 2

3. 3 : 7

4. 2 : 3

Q. A rod of length $l$ moves such that its ends $A$ and $B$ always lie on the lines $3x-y+5=0$ and $y+5=0$ respectively. The locus of the point $P,$ which divides $AB$ internally in the ratio $2:1,$ is $l^2=\frac{1}{k}(ax-by-5{)}^2+9(y+5{)}^2.$ Then

1. $k=4,a+b=6$
2. $k=3,a+b=5$
3. $k=4,a+b=0$
4. $k=3,a+b=4$

Q. Find the coordinate of points which trisect the line segment joining $(1,-2)$ and $(-3,4)$.

Q. Assertion :The value of $\left(\begin{array}{c}51\\ 3\end{array}\right)+\left(\begin{array}{c}50\\ 3\end{array}\right)+\left(\begin{array}{c}49\\ 3\end{array}\right)+\left(\begin{array}{c}48\\ 3\end{array}\right)+\left(\begin{array}{c}47\\ 3\end{array}\right)+\left(\begin{array}{c}47\\ 4\end{array}\right)$ is equal to $\left(\begin{array}{c}52\\ 4\end{array}\right)$ Reason: ${}^{n-1}{C}_r{+}^n{C}_{r+1}{=}^{n+1}{C}_{r+1}$

1. Both (A) & (R) are individually true & (R) is the correct explanation of (A),
2. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).
3. (A) is true but (R) is false,
4. (A) is false but (R) is true.

Q. If direction ratios of the normal of the plane which contains the lines $\frac{x-2}{3}=\frac{y-4}{2}=\frac{z-1}{1}\&\frac{x-6}{3}=\frac{y+2}{2}=\frac{z-2}{1}$ are $(a,1,-26)$, then $a$ is equal to

1. $5$
2. $6$
3. $7$
4. $8$

Q. The line segment joining the points (-3, -4) and (1, -2) is divided by the y-axis in the ratio

1. 1 : 3
2. 3 : 1
3. 2 : 3
4. 3 : 2

Q. The point (-17, -10) divides the line joining J(-8, -4), L(1, 2) in ratio $=$ 1:2.
If true then enter $1$ and if false then enter $0$

Q. Let $b=6$, with $a$ and $c$ satisfying (E). lf $\alpha$ and $\beta$ are the roots of the quadratic equation $a{x}^2+bx+c=0$, then $\sum _{n=0}^{\infty }{\left(\frac{1}{\alpha }+\frac{1}{\beta }\right)}^n$ is:

1. $\infty$
2. $7$
3. $6$
4. $\frac{6}{7}$

Q.

If point $P$ divides the line joining the points $(5,0)$ and $(0,4)$ in the ratio $2:3$ internally, then the $x$ coordinate of $P$ is

1. $2$
2. $1$
3. $3$
4. $4$

Q.

Find the equation of the line which passes through the point (– 4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5 : 3 by this point.

1. $3x+5y=3$
2. $9x-20y+96=0$
3. $9x+20y+96=0$
4. $9x-20y-96=0$

Q. Find the co-ordinates of a point C on AB produced such that $3AB=AC$, where $A=(3,2)$ and $B=(-2,4).$

1. $(-12,8)$
2. $(12,8)$
3. $(8,12)$
4. $(-8,12)$

Q. Find the joint equation of the line.
$x+y-3=0$ and $2x+y-1=0$.