Advertisements
Advertisements
प्रश्न
The points (3, -4) and (-6, 2) are the extremities of a diagonal of a parallelogram. If the third vertex is (-1, -3). Find the coordinates of the fourth vertex.
Advertisements
उत्तर
Let ABCD be a parallelogram in which the coordinates of the vertices are A (-2,-1); B (1, 0) and C (4, 3). We have to find the co-ordinates of the forth vertex.
Let the fourth vertex be `D(x,y)`
Since ABCD is a parallelogram, the diagonals bisect each other. Therefore the mid-point of the diagonals of the parallelogram will coincide.
Now to find the mid-point P(x,y) of two points `A(x_1, y_1)` and `B(x_2, y_2)` we use section formula as,
`P(x,y) = ((x_1+x_2)/2, (y_1+y_2)/2)`
The mid-point of the diagonals of the parallelogram will coincide.
So,
Co-ordinate of mid-point AC = Coordinate of mid-point of BD
Therefore,
`((x+1)/2, y/2) = ((4-2)/2, (3 -1)/2)`
`((x + 1)/2,y/2) = (1,1)`
Now equate the individual terms to get the unknown value. So,
x = 1
y = 2
So the forth vertex is D(1, 2)
APPEARS IN
संबंधित प्रश्न
If A(–2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides
Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:
A(-1,-2) B(1, 0), C (-1, 2), D(-3, 0)
Find the equation of the perpendicular bisector of the line segment joining points (7, 1) and (3,5).
In what ratio does the point (−4, 6) divide the line segment joining the points A(−6, 10) and B(3,−8)?
Show that the following points are the vertices of a square:
A (0,-2), B(3,1), C(0,4) and D(-3,1)
In what ratio does y-axis divide the line segment joining the points (-4, 7) and (3, -7)?
Show that the points (−2, 3), (8, 3) and (6, 7) are the vertices of a right triangle ?
Find the possible pairs of coordinates of the fourth vertex D of the parallelogram, if three of its vertices are A(5, 6), B(1, –2) and C(3, –2).
Show that ΔABC, where A(–2, 0), B(2, 0), C(0, 2) and ΔPQR where P(–4, 0), Q(4, 0), R(0, 2) are similar triangles.
If P (x, 6) is the mid-point of the line segment joining A (6, 5) and B (4, y), find y.
If the line segment joining the points (3, −4), and (1, 2) is trisected at points P (a, −2) and Q \[\left( \frac{5}{3}, b \right)\] , Then,
If A(4, 9), B(2, 3) and C(6, 5) are the vertices of ∆ABC, then the length of median through C is
A line intersects the y-axis and x-axis at P and Q , respectively. If (2,-5) is the mid-point of PQ, then the coordinates of P and Q are, respectively
The line segment joining the points (3, -1) and (-6, 5) is trisected. The coordinates of point of trisection are ______.
Students of a school are standing in rows and columns in their playground for a drill practice. A, B, C and D are the positions of four students as shown in figure. Is it possible to place Jaspal in the drill in such a way that he is equidistant from each of the four students A, B, C and D? If so, what should be his position?
The coordinates of a point whose ordinate is `-1/2` and abscissa is 1 are `-1/2, 1`.
Find the coordinates of the point whose ordinate is – 4 and which lies on y-axis.
If the coordinate of point A on the number line is –1 and that of point B is 6, then find d(A, B).
The coordinates of the point where the line 2y = 4x + 5 crosses x-axis is ______.
Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of becoming an astronaut one day. So, he started to sketch his own rocket designs on the graph sheet. One such design is given below :
Based on the above, answer the following questions:
i. Find the mid-point of the segment joining F and G. (1)
ii. a. What is the distance between the points A and C? (2)
OR
b. Find the coordinates of the points which divides the line segment joining the points A and B in the ratio 1 : 3 internally. (2)
iii. What are the coordinates of the point D? (1)
