Advertisements
Advertisements
प्रश्न
In the following, find the value of ‘a’ for which the given points are collinear
(2, 3), (4, a) and (6, – 3)
Advertisements
उत्तर
Let the points be A(2, 3), B(4, a) and C(6, – 3).
Since the given points are collinear.
Area of a triangle = 0
`1/2 [(x_1y_2 + x_2y_3 + x_3y_1) - (x_2y_1 + x_3y_2 + x_1y_3)]` = 0
`1/2[(2"a" - 12 + 18) - (12 + 6"a" - 6)]` = 0
2a + 6 – (6 + 6a) = 0
2a + 6 – 6 – 6a = 0
– 4a = 0
⇒ a = `0/4`
= 0
The value of a = 0
APPEARS IN
संबंधित प्रश्न
The area of a rectangular is 640 m2. Taking its length as x cm; find in terms of x, the width of the rectangle. If the perimeter of the rectangle is 104 m; find its dimensions.
The length of a rectangular verandah is 3 m more than its breadth. The numerical value of its area is equal to the numerical value of its perimeter.
(i) Taking x as the breadth of the verandah, write an equation in x that represents the above statement
(ii) Solve the equation obtained in (i) above and hence find the dimensions of the verandah.
Two adjacent sides of a parallelogram are 24 cm and 18 cm. If the distance between the longer sides is 12 cm; find the distance between the shorter sides.
Using the information in the following figure, find its area.
A quadrilateral field of unequal has a longer diagonal with 140m. The perpendiculars from opposite vertives upon this diagonal are 20m and 14m. Find the area of the field.
Vertices of given triangles are taken in order and their areas are provided aside. Find the value of ‘p’.
| Vertices | Area (sq.units) |
| (0, 0), (p, 8), (6, 2) | 20 |
In the following, find the value of ‘a’ for which the given points are collinear
(a, 2 – 2a), (– a + 1, 2a) and (– 4 – a, 6 – 2a)
Find the area of quadrilateral BCEG
When proving that a quadrilateral is a parallelogram by using slopes you must find
If the diagonal d of a quadrilateral is doubled and the heights h1 and h2 falling on d are halved, then the area of quadrilateral is ______.
