Advertisements
Advertisements
Question
Find the equation of the side BC of the triangle ABC whose vertices are (−1, −2), (0, 1) and (2, 0) respectively. Also, find the equation of the median through (−1, −2).
Solution
The vertices of triangle ABC are A (−1, −2), B (0, 1) and C (2, 0).
So, the equation of BC is
\[y - 1 = \frac{0 - 1}{2 - 0}\left( x - 0 \right)\]
\[ \Rightarrow y - 1 = \frac{- 1}{2}\left( x - 0 \right)\]
\[ \Rightarrow 2y - 2 = - x\]
\[ \Rightarrow x + 2y - 2 = 0\]
Let D be the midpoint of BC.
\[\therefore D \equiv \left( \frac{0 + 2}{2}, \frac{1 + 0}{2} \right) \equiv \left( 1, \frac{1}{2} \right)\]
So, the equation of median AD is
\[y + 2 = \frac{\frac{1}{2} + 2}{1 + 1}\left( x + 1 \right)\]
\[y + 2 = \frac{5}{4}\left( x + 1 \right)\]
\[ \Rightarrow 4y + 8 = 5x + 5\]
\[ \Rightarrow 5x - 4y - 3 = 0\]
APPEARS IN
RELATED QUESTIONS
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.
In the triangle ABC with vertices A (2, 3), B (4, –1) and C (1, 2), find the equation and length of altitude from the vertex A.
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 for p = 4, α = 150°.
Find the equation of the straight line upon which the length of the perpendicular from the origin is 2 and the slope of this perpendicular is \[\frac{5}{12}\].
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.
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 \[x + \sqrt{3}y - 4 = 0\] .
Reduce the following equation to the normal form and find p and α in \[x - y + 2\sqrt{2} = 0\].
Show that the origin is equidistant from the lines 4x + 3y + 10 = 0; 5x − 12y + 26 = 0 and 7x + 24y = 50.
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 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 area of the triangle formed by the line y = m1 x + c1, y = m2 x + c2 and x = 0.
Find the area of the triangle formed by the line x + y − 6 = 0, x − 3y − 2 = 0 and 5x − 3y + 2 = 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:
3x − 5y − 11 = 0, 5x + 3y − 7 = 0 and x + 2y = 0
Prove that the following sets of three lines are concurrent:
\[\frac{x}{a} + \frac{y}{b} = 1, \frac{x}{b} + \frac{y}{a} = 1\text { and } y = x .\]
Find the conditions that the straight lines y = m1 x + c1, y = m2 x + c2 and y = m3 x + c3 may meet in a point.
If a, b, c are in A.P., prove that the straight lines ax + 2y + 1 = 0, bx + 3y + 1 = 0 and cx + 4y + 1 = 0 are concurrent.
Find the equation of the perpendicular bisector of the line joining the points (1, 3) and (3, 1).
Find the equation of the right bisector of the line segment joining the points (a, b) and (a1, b1).
Find the projection of the point (1, 0) on the line joining the points (−1, 2) and (5, 4).
Write the coordinates of the orthocentre of the triangle formed by the lines xy = 0 and x + y = 1.
Write the area of the figure formed by the lines a |x| + b |y| + c = 0.
The number of real values of λ for which the lines x − 2y + 3 = 0, λx + 3y + 1 = 0 and 4x − λy + 2 = 0 are concurrent is
The equations of the sides AB, BC and CA of ∆ ABC are y − x = 2, x + 2y = 1 and 3x + y + 5 = 0 respectively. The equation of the altitude through B is
Prove that every straight line has an equation of the form Ax + By + C = 0, where A, B and C are constants.
If the intercept of a line between the coordinate axes is divided by the point (–5, 4) in the ratio 1 : 2, then find the equation of the line.
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.
For specifying a straight line, how many geometrical parameters should be known?
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.
6x + 3y – 5 = 0
Reduce the following equation into intercept form and find their intercepts on the axes.
4x – 3y = 6
