Advertisements
Advertisements
प्रश्न
Three vertices of a parallelogram taken in order are (−1, −6), (2, −5) and (7, 2). The fourth vertex is
पर्याय
(1, 4)
(4, 1)
(1, 1)
(4, 4)
(0, 0)
उत्तर
(4,1)
Let A(−1, −6), B(2, −5) and C(7, 2) be the given vertex. Let D(h, k) be the fourth vertex.
The midpoints of AC and BD are \[\left( 3, - 2 \right) \text { and } \left( \frac{2 + h}{2}, \frac{- 5 + k}{2} \right)\] respectively.
We know that the diagonals of a parallelogram bisect each other.
\[\therefore 3 = \frac{2 + h}{2} and - 2 = \frac{- 5 + k}{2}\]
\[ \Rightarrow h = 4 \text { and } k = 1\]
APPEARS IN
संबंधित प्रश्न
Find the equation of the line which satisfy the given condition:
Write the equations for the x and y-axes.
Find the equation of the line which satisfy the given condition:
Passing through the point (–4, 3) with slope `1/2`.
Find the equation of the line which satisfy the given condition:
Passing though (0, 0) with slope m.
Find the equation of the line which satisfy the given condition:
Passing though `(2, 2sqrt3)` and is inclined with the x-axis at an angle of 75°.
Find the equation of the line which satisfy the given condition:
Intersects the x-axis at a distance of 3 units to the left of origin with slope –2.
Find the equation of the line which satisfy the given condition:
Intersects the y-axis at a distance of 2 units above the origin and making an angle of 30° with the positive direction of the x-axis.
Find the equation of the line which satisfy the given condition:
Passing through the points (–1, 1) and (2, –4).
Find the equation of the line which is at a perpendicular distance of 5 units from the origin and the angle made by the perpendicular with the positive x-axis is 30°
Find the equation of the line which satisfy the given condition:
The vertices of ΔPQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the median through the vertex R.
The vertices of ΔPQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the median through the vertex R.
Find the equation of the line passing through (–3, 5) and perpendicular to the line through the points (2, 5) and (–3, 6).
Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.
The perpendicular from the origin to a line meets it at the point (– 2, 9), find the equation of the line.
By using the concept of equation of a line, prove that the three points (3, 0), (–2, –2) and (8, 2) are collinear.
Find the values of q and p, if the equation x cos q + y sinq = p is the normal form of the line `sqrt3 x` + y + 2 = 0.
If the lines y = 3x + 1 and 2y = x + 3 are equally inclined to the line y = mx + 4, find the value of m.
Classify the following pair of line as coincident, parallel or intersecting:
2x + y − 1 = 0 and 3x + 2y + 5 = 0
Classify the following pair of line as coincident, parallel or intersecting:
3x + 2y − 4 = 0 and 6x + 4y − 8 = 0.
Prove that the lines \[\sqrt{3}x + y = 0, \sqrt{3}y + x = 0, \sqrt{3}x + y = 1 \text { and } \sqrt{3}y + x = 1\] form a rhombus.
Find the equation to the straight line parallel to 3x − 4y + 6 = 0 and passing through the middle point of the join of points (2, 3) and (4, −1).
Prove that the lines 2x − 3y + 1 = 0, x + y = 3, 2x − 3y = 2 and x + y = 4 form a parallelogram.
Find the angle between the lines x = a and by + c = 0..
Find the equation of the line mid-way between the parallel lines 9x + 6y − 7 = 0 and 3x + 2y + 6 = 0.
Prove that the area of the parallelogram formed by the lines a1x + b1y + c1 = 0, a1x + b1y+ d1 = 0, a2x + b2y + c2 = 0, a2x + b2y + d2 = 0 is \[\left| \frac{\left( d_1 - c_1 \right)\left( d_2 - c_2 \right)}{a_1 b_2 - a_2 b_1} \right|\] sq. units.
Deduce the condition for these lines to form a rhombus.
Prove that the area of the parallelogram formed by the lines 3x − 4y + a = 0, 3x − 4y + 3a = 0, 4x − 3y− a = 0 and 4x − 3y − 2a = 0 is \[\frac{2}{7} a^2\] sq. units..
Show that the diagonals of the parallelogram whose sides are lx + my + n = 0, lx + my + n' = 0, mx + ly + n = 0 and mx + ly + n' = 0 include an angle π/2.
Write an equation representing a pair of lines through the point (a, b) and parallel to the coordinate axes.
