# Two Point Form of a Line

## Trending Questions

**Q.**Suppose that the points (h, k), (1, 2) and (−3, 4) lie on the line L1. If a line L2 passing through the points (h, k) and (4, 3) is perpendicular to L1, then kh equals :

- 0
- 3
- 13
- −17

**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 :

- 5x−3y+1=0
- 5x+3y−11=0
- 3x−5y+7=0
- 3x+5y−13=0

**Q.**

The inclination of the straight line passing through the point $\left(-3,6\right)$ and the midpoint of the line joining the $\left(4,-5\right)$ and $\left(-2,9\right)$ is

$\frac{\mathrm{\pi}}{4}$

$\frac{\mathrm{\pi}}{6}$

$\frac{\mathrm{\pi}}{3}$

$\frac{3\mathrm{\pi}}{4}$

**Q.**The locus represented by xy+yz=0 is

- a pair of perpendicular lines
- a pair of parallel lines
- a pair of parallel planes
- a pair of perpendicular planes

**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

- x−5y+23=0
- 7x+4y−34=0
- 8x−y+11=0
- x+3y−17=0

**Q.**

Find the equation of the straight line passing through the points$(-1,1)$ and$(2,-4)$.

**Q.**If each of the points (x1, 4), (−2, y1) lies on the line joining the points (2, −1) and (5, −3), then the point P(x1, y1) lies on the line

- 2x+6y+1=0
- 6(x+y)−25=0
- 6(x+y)+25=0
- 2x+3y−6=0

**Q.**

State whether the two lines in each of the following are parallel, perpendicular or neither:

(i) Through (5, 6) and (2, 3); through (9, -2) and (6, -5)

(ii) Through (9, 5) and (-1, 1); through (3, -5) and (8, -3)

(iii) Through (6, 3) and (1, 1); through (-2, 5) and (2, -5)

(iv) Through (3, 15) and (16, 6); through (-5, 3) and (8, 2).

**Q.**

The equation of a line passing through $(-2,-4)$ and perpendicular to the line $3x-y+5=0$ is:

$3y+x-8=0$

$3x+y+6=0$

$x+3y+14=0$

None of these

**Q.**

The equation of a straight line which passes through the point $(-3,5)$ such that the portion of it between the axes is divided by the point in the ratio $5:3$ (reckoning from the x-axis) will be

$x+y-2=0$

$2x+y+1=0$

$x+2y-7=0$

$x-y+8=0$

**Q.**The equation of the internal bisector of the angle A of a triangle ABC whose vertices are A(4, 3), B(0, 0) and C(2, 3) is

- x-3y+5=0
- x+3y-5=0
- 3x-y-9=0
- 3x+y-9=0

**Q.**

Find the equation of the side BC of the triangle ABC whose vertices are A (-1, -2), B (0, 1) and C (2, 0) respectively. Also, find the equation of the median through A (-1, -2).

**Q.**

Find the equations to the straight lines which go through the origin and trisect the portion of the straight line 3x + y = 12 which is intercepted between the axes of coordinates.

**Q.**In a triangle ABC if A≡(1, 2) and internal angle bisectors through B and C are y=x and y=−2x, then the inradius r of the △ ABC is

**Q.**

In a hyperbola the distance between the foci is three times the distance between the directories then its eccentricity is

5/2

5/4

3/2

**Q.**

Find the equation of the bisector of angle A of the triangle whose vertices are A (4, 3), B (0, 0) and C (2, 3).

**Q.**

Find the equations of the diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1.

**Q.**

The length L (in centimeters) of a copper rod is a linear function of its Celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L interms of C.

**Q.**The equation of straight line which is equidistant from the points A(2, –2), B(6, 1) and C(–3, 4) can be

- 2x+6y−5=0
- 12x+10y−43=0
- 6x−8y−11=0
- 6x−8y+11=0

**Q.**

Find the equation of the striaght lines passing through the following pair of points:

(i) (0, 0) and (2, - 2) (ii) (a, b) and ( a + c sin α, b + c cos α)

(iii) (0, - a) and (b, 0) (iv) (a, b) and (a + b, a - b) (v) (at1, a/t1) and (at2, a/t2) (vi) (a cos α, a sin α) and (a cos β, a sin β)

**Q.**

The equation of the bisector of the angle between two lines $3x-4y+12=0$ and $12x-5y+7=0,$ which contain the point $(-1,4)$ is

**Q.**

In what ratio is the line joining the points (2, 3) and (4, -5) divided by the line passing through the points (6, 8) and (-3, -2).

**Q.**

Elena and her husband Marc both drive to work. Elenas car has a current mileage (total distance driven) of $9,000$ and she drives $22,000$ $\mathrm{miles}$ more each year. Marcs car has a current mileage of $22,000$ and he drives $22,000$ $\mathrm{miles}$ more each year. Will the mileage for the two cars ever be equal? Explain.

No; The equations have different slopes, so the lines do not intersect.

Yes; The equations have different $y-$intercepts, so the lines intersect.

No; The equations have different slopes, so the lines intersect.

No; The equations have equal slopes but different $y-$intercepts, so the lines do not intersect.

**Q.**

The vertices of a quadrilateral are A (-2, 6), B (1, 2), C (10, 4) and D (7, 8). Find the equations of its diagonals.

**Q.**

A vertex of square is $\left(3,4\right)$ and diagonal $x+2y=1$, then the second diagonal which passes through given vertex will be

$2x\u2013y+2=0$

$x+2y=11$

$2x\u2013y=2$

none of these

**Q.**

Find the equation to the straight line which bisects the distance between the points (a, b), (a', b') and also bisects the distance between the points (- a, b) and a', - b).

**Q.**

Find the equations to the diagonals of the rectangle the equations of whose sides are x = a, x = a', y = b and y = b'.

**Q.**

The number of points on the line $x+y=4$, which are a unit distance apart from the line $2x+2y=5$, is

$0$

$1$

$2$

$\infty $

**Q.**

The point of intersection of the lines represented by the equation 2x2+3y2+7xy+8x+14y+8=0 is

(0, 2)

(1, 2)

(-2, 0)

(-2, 1)

**Q.**

In the triangle ABC with vertices A(2, 3), B(4, -1) and C(1, 2) find the equation and the length of the altitude from the vertex A.