Advertisements
Advertisements
प्रश्न
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).
उत्तर
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
संबंधित प्रश्न
Reduce the following equation into intercept form and find their intercepts on the axes.
3y + 2 = 0
Find equation of the line perpendicular to the line x – 7y + 5 = 0 and having x intercept 3.
Two lines passing through the point (2, 3) intersects each other at an angle of 60°. If slope of one line is 2, find equation of the other line.
Find the equation of the right bisector of the line segment joining the points (3, 4) and (–1, 2).
Find equation of the line which is equidistant from parallel lines 9x + 6y – 7 = 0 and 3x + 2y + 6 = 0.
A person standing at the junction (crossing) of two straight paths represented by the equations 2x – 3y+ 4 = 0 and 3x + 4y – 5 = 0 wants to reach the path whose equation is 6x – 7y + 8 = 0 in the least time. Find equation of the path that he should follow.
Find the equation of a line which is equidistant from the lines x = − 2 and x = 6.
Find the equation of a line making an angle of 150° with the x-axis and cutting off an intercept 2 from y-axis.
Find the equation of the right bisector of the line segment joining the points (3, 4) and (−1, 2).
Find the equation of a line for p = 5, α = 60°.
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 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 slope-intercept form and find slope and y-intercept;
Reduce the equation\[\sqrt{3}\] x + y + 2 = 0 to intercept form and find intercept on the axes.
Reduce the following equation to the normal form and find p and α in \[x + y + \sqrt{2} = 0\].
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 x + y − 6 = 0, x − 3y − 2 = 0 and 5x − 3y + 2 = 0.
Show that the area of the triangle formed by the lines y = m1 x, y = m2 x and y = c is equal to \[\frac{c^2}{4}\left( \sqrt{33} + \sqrt{11} \right),\] where m1, m2 are the roots of the equation \[x^2 + \left( \sqrt{3} + 2 \right)x + \sqrt{3} - 1 = 0 .\]
Find the orthocentre of the triangle the equations of whose sides are x + y = 1, 2x + 3y = 6 and 4x − y + 4 = 0.
Prove that the following sets of three lines are concurrent:
\[\frac{x}{a} + \frac{y}{b} = 1, \frac{x}{b} + \frac{y}{a} = 1\text { and } y = x .\]
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 a line which is perpendicular to the line \[\sqrt{3}x - y + 5 = 0\] and which cuts off an intercept of 4 units with the negative direction of y-axis.
Find the equation of the straight line which has y-intercept equal to \[\frac{4}{3}\] and is perpendicular to 3x − 4y + 11 = 0.
Find the image of the point (2, 1) with respect to the line mirror x + y − 5 = 0.
If the image of the point (2, 1) with respect to the line mirror be (5, 2), find the equation of the mirror.
Find the coordinates of the foot of the perpendicular from the point (−1, 3) to the line 3x − 4y − 16 = 0.
Find the projection of the point (1, 0) on the line joining the points (−1, 2) and (5, 4).
The equations of perpendicular bisectors of the sides AB and AC of a triangle ABC are x − y + 5 = 0 and x + 2y = 0 respectively. If the point A is (1, −2), find the equation of the line BC.
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.
Find the values of the parameter a so that the point (a, 2) is an interior point of the triangle formed by the lines x + y − 4 = 0, 3x − 7y − 8 = 0 and 4x − y − 31 = 0.
Write the coordinates of the orthocentre of the triangle formed by the lines x2 − y2 = 0 and x + 6y = 18.
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
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.
A line passes through P(1, 2) such that its intercept between the axes is bisected at P. The equation of the line 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 intercept form and find their intercepts on the axes.
3x + 2y – 12 = 0
