Advertisements
Advertisements
प्रश्न
Three vertices of a parallelogram, taken in order, are (−1, −6), (2, −5) and (7, 2). Write the coordinates of its fourth vertex.
Advertisements
उत्तर
Let \[A\left( - 1, - 6 \right), B\left( 2, - 5 \right)\text{ and }C\left( 7, 2 \right)\] be the vertices of the parallelogram ABCD.
Let the coordinates of D be (x, y).
Since, diagonals of a parallelogram bisect each other,
\[\frac{- 1 + 7}{2} = \frac{2 + x}{2}\text{ and }\frac{- 6 + 2}{2} = \frac{- 5 + y}{2}\]
\[ \Rightarrow x = 4\text{ and }y = 1\]"
Hence, the coordinates of the fourth vertex D are (4, 1).
APPEARS IN
संबंधित प्रश्न
If the line segment joining the points P (x1, y1) and Q (x2, y2) subtends an angle α at the origin O, prove that
OP · OQ cos α = x1 x2 + y1, y2
Four points A (6, 3), B (−3, 5), C (4, −2) and D (x, 3x) are given in such a way that \[\frac{\Delta DBC}{\Delta ABC} = \frac{1}{2}\]. Find x.
Find the coordinates of the centre of the circle inscribed in a triangle whose vertices are (−36, 7), (20, 7) and (0, −8).
The base of an equilateral triangle with side 2a lies along the y-axis, such that the mid-point of the base is at the origin. Find the vertices of the triangle.
Find the distance between P (x1, y1) and Q (x2, y2) when (i) PQ is parallel to the y-axis (ii) PQ is parallel to the x-axis.
Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).
Find the locus of a point equidistant from the point (2, 4) and the y-axis.
Find the equation of the locus of a point which moves such that the ratio of its distances from (2, 0) and (1, 3) is 5 : 4.
Find the locus of a point which is equidistant from (1, 3) and the x-axis.
Find the locus of a point such that the line segments with end points (2, 0) and (−2, 0) subtend a right angle at that point.
If A (−1, 1) and B (2, 3) are two fixed points, find the locus of a point P, so that the area of ∆PAB = 8 sq. units.
Find the locus of the mid-point of the portion of the line x cos α + y sin α = p which is intercepted between the axes.
What does the equation (x − a)2 + (y − b)2 = r2 become when the axes are transferred to parallel axes through the point (a − c, b)?
What does the equation (a − b) (x2 + y2) −2abx = 0 become if the origin is shifted to the point \[\left( \frac{ab}{a - b}, 0 \right)\] without rotation?
Find what the following equation become when the origin is shifted to the point (1, 1).
x2 + xy − 3x − y + 2 = 0
Find what the following equation become when the origin is shifted to the point (1, 1).
xy − x − y + 1 = 0
Find what the following equation become when the origin is shifted to the point (1, 1).
xy − y2 − x + y = 0
To what point should the origin be shifted so that the equation x2 + xy − 3x − y + 2 = 0 does not contain any first degree term and constant term?
Verify that the area of the triangle with vertices (2, 3), (5, 7) and (− 3 − 1) remains invariant under the translation of axes when the origin is shifted to the point (−1, 3).
Find what the following equation become when the origin is shifted to the point (1, 1).
xy − y2 − x + y = 0
Find what the following equation become when the origin is shifted to the point (1, 1).
xy − x − y + 1 = 0
Find the point to which the origin should be shifted after a translation of axes so that the following equation will have no first degree terms: y2 + x2 − 4x − 8y + 3 = 0
Find the point to which the origin should be shifted after a translation of axes so that the following equation will have no first degree terms: x2 + y2 − 5x + 2y − 5 = 0
Find the point to which the origin should be shifted after a translation of axes so that the following equation will have no first degree terms: x2 − 12x + 4 = 0
In Q.No. 1, write the distance between the circumcentre and orthocentre of ∆OAB.
Write the coordinates of the orthocentre of the triangle formed by points (8, 0), (4, 6) and (0, 0).
Write the coordinates of the circumcentre of a triangle whose centroid and orthocentre are at (3, 3) and (−3, 5), respectively.
Write the coordinates of the in-centre of the triangle with vertices at (0, 0), (5, 0) and (0, 12).
If the points (1, −1), (2, −1) and (4, −3) are the mid-points of the sides of a triangle, then write the coordinates of its centroid.
Write the area of the triangle with vertices at (a, b + c), (b, c + a) and (c, a + b).
