Advertisements
Advertisements
प्रश्न
Find values of k if area of triangle is 4 square units and vertices are (k, 0), (4, 0), (0, 2)
उत्तर
Area of a triangle = `1/2 abs ((x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1))`
`=> 1/2 abs ((k,0,1),(4,0,1),(0,2,1)) = pm 4`
`=> abs ((k,0,1),(4,0,1),(0,2,1)) = pm 8`
`=> (-2) abs ((k, 1),(4,1)) = pm 8 ` ...[On expanding with respect toC2]
`=> k - 4`
= `pm 4`
`=> "k" = 0, 8`
APPEARS IN
संबंधित प्रश्न
Find the values of k so that the area of the triangle with vertices (1, -1), (-4, 2k) and (-k, -5) is 24 sq. units.
Find the area of the triangle ABC with A(1, −4) and mid-points of sides through A being (2, −1) and (0, −1).
If the points A(x, 2), B(−3, −4) and C(7, − 5) are collinear, then the value of x is:
(A) −63
(B) 63
(C) 60
(D) −60
If A(−4, 8), B(−3, −4), C(0, −5) and D(5, 6) are the vertices of a quadrilateral ABCD, find its area.
Find the area of the triangle formed by joining the mid-point of the sides of the triangle whose vertices are (0, –1), (2, 1) and (0, 3). Find the ratio of area of the triangle formed to the area of the given triangle.
For what value of k are the points (k, 2 – 2k), (–k + 1, 2k) and (–4 – k, 6 – 2k) are collinear ?
The coordinates of A, B, C are (6, 3), (–3, 5) and (4, – 2) respectively and P is any point (x, y). Show that the ratio of the areas of triangle PBC and ABC is
Find the area of the triangle whose vertices are: (2, 3), (-1, 0), (2, -4)
In each of the following find the value of 'k', for which the points are collinear.
(8, 1), (k, -4), (2, -5)
Find a relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear.
Find the centre of a circle passing through the points (6, − 6), (3, − 7) and (3, 3).
If area of triangle is 35 square units with vertices (2, −6), (5, 4), and (k, 4), then k is ______.
Find the area of a triangle whose vertices are
(a, c + a), (a, c) and (−a, c − a)
Find the area of the quadrilaterals, the coordinates of whose vertices are
(−3, 2), (5, 4), (7, −6) and (−5, −4)
Find the centroid of the triangle whosw vertices is (1,4), (-1,1) and (3,2) .
Find the area of a triangle whose sides are respectively 150 cm, 120 cm and 200 cm ?
prove that the points A (7, 10), B(-2, 5) and C(3, -4) are the vertices of an isosceles right triangle.
If A(5,2), B(2, -2) and C(-2, t) are the vertices of a right triangle with ∠B=90° , then find the value of t .
Prove that the points A(2, 4), b(2, 6) and (2 +`sqrt(3)` ,5) are the vertices of an equilateral triangle
If G(-2, 1) is the centroid of a ΔABC and two of its vertices are A(1, -6) and B(-5, 2) , find the third vertex of the triangle.
Find the value of x for which points A(x, 2), B(-3, -4) and C(7, -5) are collinear.
If the centroid of ΔABC having vertices A (a,b) , B (b,c) and C (c,a) is the origin, then find the value of (a+b+c).
A field is in the shape of a right angled triangle whose base is 25 m and height 20 m. Find the cost of levelling the field at the rate of ₹ 45 per sq.m2
In a triangle ABC, if `|(1, 1, 1),(1 + sin"A", 1 + sin"B", 1 + sin"C"),(sin"A" + sin^2"A", sin"B" + sin^2"B", sin"C" + sin^2"C")|` = 0, then prove that ∆ABC is an isoceles triangle.
Show that the points (a + 5, a – 4), (a – 2, a + 3) and (a, a) do not lie on a straight line for any value of a.
The value of the determinant `abs((1,"x","x"^3),(1,"y","y"^3),(1,"z","z"^3))` is ____________.
The area of a triangle with vertices A(3, 0), B(7, 0) and C(8, 4) is ______.
The area of a triangle with vertices (a, b + c), (b, c + a) and (c, a + b) is ______.
Find the value of m if the points (5, 1), (–2, –3) and (8, 2m) are collinear.
Find the values of k if the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k – 1, 5k) are collinear.
Find the missing value:
| Base | Height | Area of parallelogram |
| ______ | 15 cm | 154.5 cm2 |
The area of a triangle with vertices A, B, C is given by ______.
In the given figure, ratio of the area of triangle ABC to the area of triangle ACD is the same as the ratio of base BC of triangle ABC to the base CD of ΔACD.
Triangles having the same base have equal area.
In the given figure, triangle AEC is right-angled at E, B is a point on EC, BD is the altitude of triangle ABC, AC = 25 cm, BC = 7 cm and AE = 15 cm. Find the area of triangle ABC and the length of DB.
Find the missing value:
| Base | Height | Area of Triangle |
| ______ | 31.4 mm | 1256 mm2 |
