Advertisements
Advertisements
प्रश्न
Show that the points A(2,1), B(5,2), C(6,4) and D(3,3) are the angular points of a parallelogram. Is this figure a rectangle?
Advertisements
उत्तर
The given points are s A(2,1), B(5,2), C(6,4) and D(3,3)
`AB = sqrt((5-2)^2 +(2-1)^2 ) = sqrt((3)^2 +(1)^2 ) = sqrt(9+1) = sqrt(10) ` units
`BC = sqrt((6-5)^2 +(4-2)^2 )= sqrt((1)^2 +(2)^3) = sqrt(1+4) = sqrt(5) `units
`CD = sqrt((3-6)^2 +(3-4)^2) = sqrt((-3)^2 +(-1)^2) = sqrt(9+1) = sqrt(10) `units
`AD = sqrt((3-2)^2+(3-1)^2) = sqrt((1)^2 +(2)^2) = sqrt(1+4) = sqrt(5) ` units
Thus, AB = CD = `sqrt(10) "units and " BC= AD = sqrt(5) ` units
So, quadrilateral ABCD is a parallelogram
`Also , AC = sqrt((6-2)^2 +(4-1)^2) = sqrt((4)^2 +(3)^2 )= sqrt(16+9) = sqrt(25) = 5 ` units
`BD = sqrt((3-5) ^2 +(3-2)^2 ) = sqrt((-2)^2 +(1)^2) = sqrt(4+1) = sqrt(5) units `
But diagonal AC is not equal to diagonal BD. Hence, the given points do not form a rectangle.
APPEARS IN
संबंधित प्रश्न
If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k − 1, 5k) are collinear, then find the value of k
On which axis do the following points lie?
S(0,5)
The coordinates of the point P are (−3, 2). Find the coordinates of the point Q which lies on the line joining P and origin such that OP = OQ.
Find the centre of the circle passing through (5, -8), (2, -9) and (2, 1).
Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:
A(4, 5) B(7, 6), C (4, 3), D(1, 2)
Prove that the points (4, 5) (7, 6), (6, 3) (3, 2) are the vertices of a parallelogram. Is it a rectangle.
Find the coordinates of the points which divide the line segment joining the points (-4, 0) and (0, 6) in four equal parts.
Find the coordinates of the midpoints of the line segment joining
A(3,0) and B(-5, 4)
The base QR of a n equilateral triangle PQR lies on x-axis. The coordinates of the point Q are (-4, 0) and origin is the midpoint of the base. Find the coordinates of the points P and R.
Two points having same abscissae but different ordinate lie on
Find the value of k, if the points A (8, 1) B(3, −4) and C(2, k) are collinear.
If the points A(1, –2), B(2, 3) C(a, 2) and D(– 4, –3) form a parallelogram, find the value of a and height of the parallelogram taking AB as base.
What is the area of the triangle formed by the points O (0, 0), A (6, 0) and B (0, 4)?
The area of the triangle formed by (a, b + c), (b, c + a) and (c, a + b)
The ratio in which (4, 5) divides the join of (2, 3) and (7, 8) is
The length of a line segment joining A (2, −3) and B is 10 units. If the abscissa of B is 10 units, then its ordinates can be
If A(x, 2), B(−3, −4) and C(7, −5) are collinear, then the value of x is
If the coordinates of the two points are P(–2, 3) and Q(–3, 5), then (abscissa of P) – (abscissa of Q) is ______.
Find the coordinates of the point which lies on x and y axes both.
