Advertisements
Advertisements
प्रश्न
The area of a triangle with vertices (–3, 0), (3, 0) and (0, k) is 9 sq.units. The value of k will be ______.
पर्याय
9
±3
– 9
6
उत्तर
The area of a triangle with vertices (–3, 0), (3, 0) and (0, k) is 9 sq.units. The value of k will be ±3.
Explanation:
We know that, area of triangle with vertices (x1, y1), (x2, y2) and (x3, y3) is given by
Δ = `1/2|(x_1, y_1, 1),(x_2, y_2, 1),(x_3, y_3, 1)|`
∴ Area of triangle with verticles (–3, 0), (3, 0) and (0, k) is
∴ Δ = `1/2|(-3, 0, 1),(3, 0, 1),(0, "k", 1)|` = 9 ...(Given)
⇒ `[-3(-"k") - 0 + 1(3"k")]` = ±18
⇒ 6k = ±18
∴ k = `+- 18/6` = ±3
संबंधित प्रश्न
The class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular grassy lawn in the plot as shown in the following figure. The students are to sow seeds of flowering plants on the remaining area of the plot.
(i) Taking A as origin, find the coordinates of the vertices of the triangle.
(ii) What will be the coordinates of the vertices of Δ PQR if C is the origin?
Also calculate the areas of the triangles in these cases. What do you observe?
Find the area of a triangle with vertices at the point given in the following:
(2, 7), (1, 1), (10, 8)
Find the area of a triangle whose vertices are
(6,3), (-3,5) and (4,2)
The four vertices of a quadrilateral are (1, 2), (−5, 6), (7, −4) and (k, −2) taken in order. If the area of the quadrilateral is zero, find the value of k.
Show that the following sets of points are collinear.
(2, 5), (4, 6) and (8, 8)
If the coordinates of the mid-points of the sides of a triangle are (1, 1), (2, —3) and (3, 4), find the vertices of the triangle.
prove that the points A (7, 10), B(-2, 5) and C(3, -4) are the vertices of an isosceles right triangle.
Show that the points (-3, -3),(3,3) and C (-3 `sqrt(3) , 3 sqrt(3))` are the vertices of an equilateral triangle.
Show that the points A (3,1) , B (0,-2) , C(1,1) and D (4,4) are the vertices of parallelogram ABCD.
Show that the following points are collinear:
A(-5,1), B(5, 5) and C(10, 7)
For what value of x are the points A(-3, 12), B(7, 6) and C(x, 9) collinear.
For what value of y, are the points P(1, 4), Q(3,y) and R(-3, 16) are collinear ?
Find the value of y for which the points A(-3, 9), B(2,y) and C(4,-5) are collinear.
For what values of k are the points A(8, 1) B(3, -2k) and C(k, -5) collinear.
Find a relation between x and y, if the points A(2, 1), B(x, y) and C(7,5) are collinear.
If the area of triangle ABC formed by A(x, y), B(1, 2) and C(2, 1) is 6 square units, then prove that x + y = 15 ?
Using integration, find the area of the triangle whose vertices are (2, 3), (3, 5) and (4, 4).
What is the area of a triangle with base 4.8 cm and height 3.6 cm?
If the sides of a triangle are 3 cm, 4 cm and 5 cm, then the area is
If A, B, C are the angles of a triangle, then ∆ = `|(sin^2"A", cot"A", 1),(sin^2"B", cot"B", 1),(sin^2"C", cot"C", 1)|` = ______.
If the points (a1, b1), (a2, b2) and(a1 + a2, b1 + b2) are collinear, then ____________.
The area of a triangle with vertices A(3, 0), B(7, 0) and C(8, 4) is ______.
The area of the triangle whose vertices are A(1, 2), B(-2, 3) and C(-3, -4) is ______.
Points A(–6, 10), B(–4, 6) and C(3, –8) are collinear such that AB = `2/9` AC.
Find the values of k if the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k – 1, 5k) are collinear.
In the given figure, if PR = 12 cm, QR = 6 cm and PL = 8 cm, then QM is ______.
