Advertisements
Advertisements
प्रश्न
The three vertices of a parallelogram are (3, 4) (3, 8) and (9, 8). Find the fourth vertex.
Advertisements
उत्तर
Let A(3,4), B(3,8) and C(9,8) be the three given vertex then the fourth vertex D(x,y)
Since ABCD is a parallelogram, the diagonals bisect each other.
Therefore the mid-point of diagonals of the parallelogram coincide.
Let p(x,y) be the mid-point of diagonals AC then,
`P(x,y) = ((3 + 9)/2, (4 + 8)/2)`
P(x,y) = (6,6)
Let Q(x,y) be the mid point of diagonal BD. then
`Q(x,y) = ((3 + x)/2, (8 + y)/2)`
Coordinates of mid-point AC = Coordinates of mid-point BD
P(x,y) = Q(x,y)
`=> (6,6) = ((3 + x)/2, (8 + y)/2)`
Now equating individual components
`=> 6 = (3 + x)/2` and `6 = (8 + 4)/2`
=> 3 + x = 12 and 8 + y = 12
=> x = 9 and y = 4
Hence, coordinates of fourth points are (9, 4)
APPEARS IN
संबंधित प्रश्न
(Street Plan): A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.
All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines.
There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : If the 2nd street running in the North - South direction and 5th in the East - West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:
- how many cross - streets can be referred to as (4, 3).
- how many cross - streets can be referred to as (3, 4).
If G be the centroid of a triangle ABC, prove that:
AB2 + BC2 + CA2 = 3 (GA2 + GB2 + GC2)
Find the coordinates of the midpoints of the line segment joining
A(3,0) and B(-5, 4)
Find the ratio in which the point (-1, y) lying on the line segment joining points A(-3, 10) and (6, -8) divides it. Also, find the value of y.
Find the area of quadrilateral ABCD whose vertices are A(-3, -1), B(-2,-4) C(4,-1) and D(3,4)
A point whose abscissa is −3 and ordinate 2 lies in
Prove hat the points A (2, 3) B(−2,2) C(−1,−2), and D(3, −1) are the vertices of a square ABCD.
If the point \[C \left( - 1, 2 \right)\] divides internally the line segment joining the points A (2, 5) and B( x, y ) in the ratio 3 : 4 , find the value of x2 + y2 .
The points \[A \left( x_1 , y_1 \right) , B\left( x_2 , y_2 \right) , C\left( x_3 , y_3 \right)\] are the vertices of ΔABC .
(i) The median from A meets BC at D . Find the coordinates of the point D.
(ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1.
(iii) Find the points of coordinates Q and R on medians BE and CF respectively such thatBQ : QE = 2 : 1 and CR : RF = 2 : 1.
(iv) What are the coordinates of the centropid of the triangle ABC ?
If the points A(−1, −4), B(b, c) and C(5, −1) are collinear and 2b + c = 4, find the values of b and c.
A line segment is of length 10 units. If the coordinates of its one end are (2, −3) and the abscissa of the other end is 10, then its ordinate is
If points (t, 2t), (−2, 6) and (3, 1) are collinear, then t =
If P(2, 4), Q(0, 3), R(3, 6) and S(5, y) are the vertices of a parallelogram PQRS, then the value of y is
If segment AB is parallel Y-axis and coordinates of A are (1, 3), then the coordinates of B are ______.
The line 3x + y – 9 = 0 divides the line joining the points (1, 3) and (2, 7) internally in the ratio ______.
A point both of whose coordinates are negative will lie in ______.
Points (1, – 1), (2, – 2), (4, – 5), (– 3, – 4) ______.
Find the coordinates of the point which lies on x and y axes both.
In which quadrant, does the abscissa, and ordinate of a point have the same sign?
Co-ordinates of origin are ______.
