Advertisements
Advertisements
Question
Find the equation of the right bisector of the line segment joining the points (a, b) and (a1, b1).
Solution
Let A (a, b) and B (a1, b1) be the given points. Let C be the midpoint of AB.
\[\therefore\text { Coordinates of C } = \left( \frac{a + a_1}{2}, \frac{b + b_1}{2} \right)\]
And, slope of AB = \[\frac{b_1 - b}{a_1 - a}\]
So, the slope of the right bisector of AB is \[- \frac{a_1 - a}{b_1 - b}\]
Thus, the equation of the right bisector of the line segment joining the points (a, b) and (a1, b1) is
\[y - \frac{b + b_1}{2} = - \frac{a_1 - a}{b_1 - b}\left( x - \frac{a + a_1}{2} \right)\]
\[ \Rightarrow 2\left( a_1 - a \right)x + 2y\left( b_1 - b \right) + \left( a^2 + b^2 \right) - \left( {a_1}^2 + {b_1}^2 \right) = 0 \]
This is equation of the required line .
APPEARS IN
RELATED QUESTIONS
Reduce the following equation into intercept form and find their intercepts on the axes.
3y + 2 = 0
Reduce the following equation into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis.
`x – sqrt3y + 8 = 0`
Find equation of the line parallel to the line 3x – 4y + 2 = 0 and passing through the point (–2, 3).
Find the equation of a line which makes an angle of tan−1 (3) with the x-axis and cuts off an intercept of 4 units on negative direction of y-axis.
Find the equation of the line which intercepts a length 2 on the positive direction of the x-axis and is inclined at an angle of 135° with the positive direction of y-axis.
Point R (h, k) divides a line segment between the axes in the ratio 1 : 2. Find the equation of the line.
Find the equation of a line for p = 8, α = 225°.
Find the equation of the line on which the length of the perpendicular segment from the origin to the line is 4 and the inclination of the perpendicular segment with the positive direction of x-axis is 30°.
Find the value of θ and p, if the equation x cos θ + y sin θ = p is the normal form of the line \[\sqrt{3}x + y + 2 = 0\].
Find the equation of a straight line on which the perpendicular from the origin makes an angle of 30° with x-axis and which forms a triangle of area \[50/\sqrt{3}\] with the axes.
If the straight line through the point P (3, 4) makes an angle π/6 with the x-axis and meets the line 12x + 5y + 10 = 0 at Q, find the length PQ.
Reduce the equation \[\sqrt{3}\] x + y + 2 = 0 to slope-intercept form and find slope and y-intercept;
Reduce the following equation to the normal form and find p and α in \[x - y + 2\sqrt{2} = 0\].
Put the equation \[\frac{x}{a} + \frac{y}{b} = 1\] to the slope intercept form and find its slope and y-intercept.
Find the values of θ and p, if the equation x cos θ + y sin θ = p is the normal form of the line \[\sqrt{3}x + y + 2 = 0\].
Find the point of intersection of the following pairs of lines:
bx + ay = ab and ax + by = ab.
Find the area of the triangle formed by the line y = 0, x = 2 and x + 2y = 3.
Find the equations of the medians of a triangle, the equations of whose sides are:
3x + 2y + 6 = 0, 2x − 5y + 4 = 0 and x − 3y − 6 = 0
Find the equation of the line joining the point (3, 5) to the point of intersection of the lines 4x + y − 1 = 0 and 7x − 3y − 35 = 0.
Prove that the following sets of three lines are concurrent:
15x − 18y + 1 = 0, 12x + 10y − 3 = 0 and 6x + 66y − 11 = 0
Prove that the following sets of three lines are concurrent:
3x − 5y − 11 = 0, 5x + 3y − 7 = 0 and x + 2y = 0
For what value of λ are the three lines 2x − 5y + 3 = 0, 5x − 9y + λ = 0 and x − 2y + 1 = 0 concurrent?
If the three lines ax + a2y + 1 = 0, bx + b2y + 1 = 0 and cx + c2y + 1 = 0 are concurrent, show that at least two of three constants a, b, c are equal.
Find the equation of the perpendicular bisector of the line joining the points (1, 3) and (3, 1).
Find the image of the point (2, 1) with respect to the line mirror x + y − 5 = 0.
Find the coordinates of the foot of the perpendicular from the point (−1, 3) to the line 3x − 4y − 16 = 0.
Find the values of α so that the point P (α2, α) lies inside or on the triangle formed by the lines x − 5y+ 6 = 0, x − 3y + 2 = 0 and x − 2y − 3 = 0.
Write the area of the figure formed by the lines a |x| + b |y| + c = 0.
The figure formed by the lines ax ± by ± c = 0 is
Two vertices of a triangle are (−2, −1) and (3, 2) and third vertex lies on the line x + y = 5. If the area of the triangle is 4 square units, then the third vertex is
If the lines x + q = 0, y − 2 = 0 and 3x + 2y + 5 = 0 are concurrent, then the value of q will be
If the line `x/"a" + y/"b"` = 1 passes through the points (2, –3) and (4, –5), then (a, b) is ______.
For specifying a straight line, how many geometrical parameters should be known?
Reduce the following equation into slope-intercept form and find their slopes and the y-intercepts.
y = 0
Reduce the following equation into intercept form and find their intercepts on the axes.
3x + 2y – 12 = 0
