Advertisements
Advertisements
प्रश्न
Find the equation of the right bisector of the line segment joining the points A (1, 0) and B (2, 3).
उत्तर
The given points are A (1, 0) and B (2, 3).
Let M be the midpoint of AB.
\[\therefore \text { Coordinates of } M = \left( \frac{1 + 2}{2}, \frac{0 + 3}{2} \right) = \left( \frac{3}{2}, \frac{3}{2} \right)\]
And, slope of AB = \[\frac{3 - 0}{2 - 1} = 3\]
Let m be the slope of the perpendicular bisector of the line joining the points A (1, 0) and B (2, 3).
\[\therefore m \times \text { Slope of AB } = - 1\]
\[ \Rightarrow m \times 3 = - 1\]
\[ \Rightarrow m = - \frac{1}{3}\]
So, the equation of the line that passes through \[M \left( \frac{3}{2}, \frac{3}{2} \right)\] and has slope \[- \frac{1}{3}\] is
\[y - \frac{3}{2} = - \frac{1}{3}\left( x - \frac{3}{2} \right)\]
\[ \Rightarrow x + 3y - 6 = 0\]
Hence, the equation of the right bisector of the line segment joining the points A (1, 0) and B (2, 3) is \[x + 3y - 6 = 0\].
APPEARS IN
संबंधित प्रश्न
Find the equation of the right bisector of the line segment joining the points (3, 4) and (–1, 2).
The perpendicular from the origin to the line y = mx + c meets it at the point (–1, 2). Find the values of m and c.
Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and –6, respectively.
If three lines whose equations are y = m1x + c1, y = m2x + c2 and y = m3x + c3 are concurrent, then show that m1(c2 – c3) + m2 (c3 – c1) + m3 (c1 – c2) = 0.
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 a line that has y-intercept −4 and is parallel to the line joining (2, −5) and (1, 2).
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.
Find the equations of the sides of the triangles the coordinates of whose angular point is respectively (1, 4), (2, −3) and (−1, −2).
Find the equations of the diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y =1.
Find the equation of a line for p = 8, α = 300°.
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 equation of the straight line on which the length of the perpendicular from the origin is 2 and the perpendicular makes an angle α with x-axis such that sin α = \[\frac{1}{3}\].
Find the equation of the straight line which makes a triangle of area \[96\sqrt{3}\] with the axes and perpendicular from the origin to it makes an angle of 30° with Y-axis.
Reduce the equation\[\sqrt{3}\] x + y + 2 = 0 to intercept form and find intercept on the axes.
Reduce the equation \[\sqrt{3}\] x + y + 2 = 0 to the normal form and find p and α.
Reduce the following equation to the normal form and find p and α in x − 3 = 0.
Find the point of intersection of the following pairs of lines:
2x − y + 3 = 0 and x + y − 5 = 0
Find the coordinates of the vertices of a triangle, the equations of whose sides are
y (t1 + t2) = 2x + 2a t1t2, y (t2 + t3) = 2x + 2a t2t3 and, y (t3 + t1) = 2x + 2a t1t3.
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.
Find the coordinates of the incentre and centroid of the triangle whose sides have the equations 3x− 4y = 0, 12y + 5x = 0 and y − 15 = 0.
Prove that the following sets of three lines are concurrent:
3x − 5y − 11 = 0, 5x + 3y − 7 = 0 and x + 2y = 0
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 projection of the point (1, 0) on the line joining the points (−1, 2) and (5, 4).
If a ≠ b ≠ c, write the condition for which the equations (b − c) x + (c − a) y + (a − b) = 0 and (b3 − c3) x + (c3 − a3) y + (a3 − b3) = 0 represent the same line.
Write the area of the figure formed by the lines a |x| + b |y| + c = 0.
A (6, 3), B (−3, 5), C (4, −2) and D (x, 3x) are four points. If ∆ DBC : ∆ ABC = 1 : 2, then x is equal to
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
Find the equation of a line which passes through the point (2, 3) and makes an angle of 30° with the positive direction of x-axis.
The inclination of the line x – y + 3 = 0 with the positive direction of x-axis is ______.
A line passes through P(1, 2) such that its intercept between the axes is bisected at P. The equation of the line is ______.
Find the equation of the straight line which passes through the point (1, – 2) and cuts off equal intercepts from axes.
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.
If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes is (3, 2), then the equation of the line will be ______.
The line which cuts off equal intercept from the axes and pass through the point (1, –2) is ______.
Locus of the mid-points of the portion of the line x sin θ + y cos θ = p intercepted between the axes is ______.
Reduce the following equation into slope-intercept form and find their slopes and the y-intercepts.
x + 7y = 0
