Advertisements
Advertisements
Question
Three vertices of a parallelogram taken in order are (−1, −6), (2, −5) and (7, 2). The fourth vertex is
Options
(1, 4)
(4, 1)
(1, 1)
(4, 4)
(0, 0)
Solution
(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
RELATED QUESTIONS
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 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 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.
A line perpendicular to the line segment joining the points (1, 0) and (2, 3) divides it in the ratio 1:n. Find the equation of the line.
Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).
Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.
Find equation of the line through the point (0, 2) making an angle `(2pi)/3` with the positive x-axis. Also, find the equation of line parallel to it and crossing the y-axis at a distance of 2 units below the origin.
The perpendicular from the origin to a line meets it at the point (– 2, 9), find the equation of the line.
The length L (in centimetre) of a copper rod is a linear function of its Celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in terms of C
Point R (h, k) divides a line segment between the axes in the ratio 1:2. Find equation of the line.
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.
Find the area of the triangle formed by the lines y – x = 0, x + y = 0 and x – k = 0.
Find the image of the point (3, 8) with respect to the line x + 3y = 7 assuming the line to be a plane mirror.
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:
x − y = 0 and 3x − 3y + 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).
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.
Show that the point (3, −5) lies between the parallel lines 2x + 3y − 7 = 0 and 2x + 3y + 12 = 0 and find the equation of lines through (3, −5) cutting the above lines at an angle of 45°.
Let ABC be a triangle with A(–3, 1) and ∠ACB = θ, 0 < θ < `π/2`. If the equation of the median through B is 2x + y – 3 = 0 and the equation of angle bisector of C is 7x – 4y – 1 = 0, then tan θ is equal to ______.
