Advertisements
Advertisements
प्रश्न
Three vertices of parallelogram ABCD taken in order are A(3, 6), B(5, 10) and C(3, 2)
1) the coordinate of the fourth vertex D
2) length of diagonal BD
3) equation of the side AD of the parallelogram ABCD
उत्तर
Three vertices of a parallelogram taken in order are A(3, 6), B(5, 10) and C(3, 2)
1) We need to find the coordinates of D.
We know that the diagonals of a parallelogram bisect each other.
Let x, y be the coordinates of D.
∴ Mid-point of diagonal AC = `((3+3)/2, (6+2)/2) = (3,4)`
And midpoint of diagonal BD = `((5+x)/2, (10 + y)/2)`
Thus we have
`(5 + x)/2 = 3` and `(10 + y)/2 = 4`
`=> 5 + x = 6` and `10 + y = 8`
=> x = 1 and y = -2
`:. D = (1,-2)`
2) Lenght of diagonal BD = `sqrt((1 - 5)^2 + (-2-10)^2)`
`= sqrt((-4)^2 + (-12)^2)`
`= sqrt(16 + 144)`
`= sqrt(160)`
`= 4sqrt10`
3) A(3,6) = `(x_1. y_1)` and B(5,10) = `(x_2, y_2)`
Slope of line AB = `m(y_2 - y_1)/(x_2 - x_1) = (10 - 6)/(5-3) = 4/2 = 2`
∴ Equation of line AB is given by
`y - y_1 = m(x - x_1)`
`=> y - 6 = 2(x - 3)`
`=> y - 6 = 2x - 6`
`=> 2x - y = 0`
`=> 2x = y`
APPEARS IN
संबंधित प्रश्न
In the given figure ABCD is a rectangle. It consists of a circle and two semi-circles each of
which are of radius 5 cm. Find the area of the shaded region. Give your answer correct to
three significant figures
Use graph paper for this question (Take 2 cm = 1 unit along both x and y-axis). ABCD is a quadrilateral whose vertices are A(2, 2), B(2, –2), C(0, –1) and D(0, 1).
1) Reflect quadrilateral ABCD on the y-axis and name it as A'B'CD
2) Write down the coordinates of A' and B'.
3) Name two points which are invariant under the above reflection
4) Name the polygon A'B'CD
A straight line passes through the points P(–1, 4) and Q(5, –2). It intersects the co-ordinate axes at points A and B. M is the mid-point of the segment AB. Find:
- The equation of the line.
- The co-ordinates of A and B.
- The co-ordinates of M.
(1, 5) and (–3, –1) are the co-ordinates of vertices A and C respectively of rhombus ABCD. Find the equations of the diagonals AC and BD.
A line through origin meets the line x = 3y + 2 at right angles at point X. Find the co-ordinates of X.
O(0, 0), A(3, 5) and B(−5, −3) are the vertices of triangle OAB. Find the equation of altitude of triangle OAB through vertex B.
Use a graph sheet for this question.
Take 1 cm = 1 unit along both x and y axis.
(i) Plot the following points:
A(0,5), B(3,0), C(1,0) and D(1,–5)
(ii) Reflect the points B, C and D on the y axis and name them as B',C'andD' respectively.
(iii) Write down the coordinates of B',C 'and D'
(iv) Join the point A, B, C, D, D ', C ', B', A in order and give a name to the closed figure ABCDD'C'B
A line is of length 10 units and one end is at the point (2, – 3). If the abscissa of the other end be 10, prove that its ordinate must be 3 or – 9.
Use a graph sheet for this question, take 2 cm = 1 unit along both x and y-axis:
- Plot the points A (3, 2) and B (5, 0). Reflect point A on the y-axis to A΄. Write co-ordinates of A΄.
- Reflect point B on the line AA΄ to B΄. Write the co-ordinates of B΄.
- Name the closed figure A’B’AB.
