Two Point Form of a Line

Q. The equation of the median through the vertex $A$ of triangle $ABC$ whose vertices are $A(2,5),B(-4,9)$ and $C(-2,-1)$ is

1. $x-5y+23=0$
2. $7x+4y-34=0$
3. $8x-y+11=0$
4. $x+3y-17=0$

Q. If $t_1$ and $t_2$ are the roots of the equation $t^2+\lambda t+1=0$, where $\lambda$ is a parameter, then the line joining the points $(a{t}_1^2,2a{t}_1)$ and $(a{t}_2^2,2a{t}_2)$ always passes through

1. $(a,0)$
2. $(-a,0)$
3. $(\lambda ,0)$
4. $(-\lambda ,0)$

Q. If in a parallelogram $ABDC$, the coordinates of $A,B$ and $C$ are respectively $(1,2),(3,4)$ and $(2,5)$, then the equation of the diagonal $AD$ is :

1. $5x+3y-11=0$
2. $5x-3y+1=0$
3. $3x-5y+7=0$
4. $3x+5y-13=0$

Q.

Find the slope of the line which passes through the origin and the midpoint of the line segment joining the points $P(0,-4)andB(8,0)$

Q. The equation of the median through the vertex $A$ of triangle $ABC$ whose vertices are $A(2,5),B(-4,9)$ and $C(-2,-1)$ is

1. $x-5y+23=0$
2. $7x+4y-34=0$
3. $8x-y+11=0$
4. $x+3y-17=0$

Q. Suppose that the points $(h,k),(1,2)$ and $(-3,4)$ lie on the line $L_1$. If a line $L_2$ passing through the points $(h,k)$ and $(4,3)$ is perpendicular to $L_1$, then $\frac{k}{h}$ equals :

1. $\frac{1}{3}$
2. $3$
3. $0$
4. $-\frac{1}{7}$

Q. Let $PS$ be the median of a triangle with vertices $P(2,2),$ $Q(6,-1)$ and $R(7,3).$ The equation of the line passing through $(1,-1)$ and parallel to $PS$ is

1. $2x-9y-7=0$
2. $2x-9y-11=0$
3. $2x+9y-11=0$
4. $2x+9y+7=0$

Q. Let the line $3x+2y=24$ meet $y-$axis at $A$ and $x-$axis at $B.$ If the perpendicular bisector of $AB$ meets the line $y=-1$ at $C,$ then the area of the $△ABC$ (in sq. units) is

Q. Suppose that the points $(h,k),(1,2)$ and $(-3,4)$ lie on the line $L_1$. If a line $L_2$ passing through the points $(h,k)$ and $(4,3)$ is perpendicular to $L_1$, then $\frac{k}{h}$ equals :

1. $\frac{1}{3}$
2. $3$
3. $0$
4. $-\frac{1}{7}$

Q.

A(-1, 8), B(4, -2) and C(-5, -3) are the vertices of a triangle, find the equation of the median through (-1, 8).

1. 21x + y + 13 = 0

2. 2x + y - 6 = 0

3. 11x - 4y + 43 = 0

4. x - 9y - 22 = 0