List of top Mathematics Questions on Straight lines

The straight line passing through the points $(1, 5)$ and $(3, -5)$ meets the coordinate axes at the points $A$ and $B$. Then the area of the triangle $\triangle OAB$, where $O$ is the origin, is

If the equation of the straight line passing through the points $(3, -4)$ and $(4, a)$ is $x - y = 7$, then the value of $a$ is equal to

A point C lies on the perpendicular bisector of the straight-line segment joining the points A(-3,-6) and B(13,-6). If the point C lies in the first quadrant and the distance between the point C and the midpoint of AB is 8 units, then the coordinates of C are

Let A(-4,3), B(0,5) and C(-1,2) be three points. The equation of the straight line which passes through C and bisects the straight-line segment AB is

If the image of the point (2,6) in the line \(x-3y+10=0\) is (h,k), then \(2h-k=\)

Assuming that the straight line works as a plane mirror for a point, the image of the point \((1,2)\) in the line \[ x-3y+4=0 \] is

The orthocentre of the triangle formed by the following straight lines is \[ y=x,\qquad x-2y+1=0,\qquad 3x-4y-1=0 \]

If the inclination of a straight line \[ x-y+1=0 \] with another straight line \(L\) is \(30^\circ\) and \(m\) is the slope of line \(L\), then \[ m^2+1= \]

If \(A(2,1)\), \(B(4,k)\), \(C(3,4)\) are vertices of triangle right angled at B and \(k\) is not an odd number, then equation of line joining orthocentre and circumcentre is

The equation of the lines through \( (1, 1) \) and making angles of \( 45^\circ \) with the line \( x + y = 0 \) are:

Let the line \(L_1 : x + 3 = 0\) intersect the lines \(L_2 : x - y = 0\) and \(L_3 : 3x + y = 0\) at the points A and B, respectively. Let the bisector of the obtuse angle between the lines \(L_2\) and \(L_3\) intersect the line \(L_1\) at the point C. Then \(BC^2 : AC^2\) is equal to:

The distance of the point $(1, 2)$ from the line $3x + 4y - 32 = 0$ measured parallel to the line $x - y = 0$ is:

The foot of the perpendicular from the point $(1, 3)$ to the line $x + y - 2 = 0$ is:

If the straight lines $x + 2y - 9 = 0$, $3x + 5y - 5 = 0$ and $ax + by - 1 = 0$ are concurrent, then the straight line $22x - 35y = 1$ passes through the point:

The distance between the parallel lines $5x + 12y - 3 = 0$ and $5x + 12y + 10 = 0$ is:

If slope of two lines represented by \( \dfrac{x^2}{a}+\dfrac{2xy}{h}+\dfrac{y^2}{b}=0 \) is twice the other, then \(ab:h^2=\ ?\)

The distance from the origin to the image of $(1, 1)$ with respect to the line $x + y + 5 = 0$ is:

A line \(L\) passes through the point of intersection of the lines \(3x+y-10=0\) and \(x-y-2=0\). If the perpendicular distance of the line \(L\) from the point \((5,1)\) is exactly \(\dfrac{2}{\sqrt{5}}\) units, which of the following represents the equation of line \(L\)?

Let point \( Q \) be the image of point \( P(2,-1) \) in the line \[ 3x+5=4y. \] Find the area of the circle that has the segment \( PQ \) as the diameter.

Area of Triangle with point (1,2) (3,6) (5,10) is

The point dividing (1, 2) and (5, 6) in ratio 1:3 internally

The x-intercept and y-intercept of a line are three times and four times of the x-intercept and y-intercept of the line $3x+2y=6$, respectively. Then the equation of the line is

If the foot of the perpendicular drawn from the origin to the line $y=mx+c$ is $(1,1)$ then the value of $m$ and $c$ are, respectively,

The perpendicular drawn from the origin to the straight line $\sqrt{3}x + y - 24 = 0$ makes an angle $\alpha$ with the positive direction of x-axis. Then $\alpha$ is equal to:

A straight line makes $y$-intercept of 5. If the angle made by the line with $y$-axis is $60^\circ$ and the line intersects $x$-axis in the negative direction, then the equation of the line is