Advertisements
Advertisements
प्रश्न
The area of a triangle is 5 sq. units. Two of its vertices are (2, 1) and (3, −2). The third vertex is (x, y) where y = x + 3. Find the coordinates of the third vertex.
Advertisements
उत्तर
Let the vertices A(2, 1), B(3, –2) and C(x, y)
Area of a triangle = 5 sq. units
`1/2[x_1y_2 + x_2y_3 + x_3y_1 - (x_2y_1 + x_3y_2 + x_1y_3)]` = 5
`1/2[- 4 + 3y + x - (3 - 2x + 2y)]` = 5
– 4 + 3y + x – 3 + 2x – 2y = 10
3x + y – 7 = 10
3x + y = 17 ...(1)
Given y = x + 3
Substitute the value ofy = x + 3 in (1)
3x + x + 3 = 17
4x = 17 – 3
4x = 14
x = `14/4 = 7/2`
Substitute the value of x in y = x + 3
y = `7/2 + 3`
⇒ y = `(7 + 6)/2`
= `13/2`
∴ The coordinates of the third vertex is `(7/2, 13/2)`
APPEARS IN
संबंधित प्रश्न
The lengths of the sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 144 cm. Find the area of the triangle and the height corresponding to the longest side.
Find the area of a quadrilateral ABCD in which AB = 42 cm, BC = 21 cm, CD = 29 cm, DA =34 cm and diagonal BD =20 cm.
The adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram.
Some measures are given in the adjacent figure, find the area of ☐ABCD.
Determine whether the sets of points are collinear?
`(-1/2, 3), (-5, 6) and (-8, 8)`
Determine whether the sets of points are collinear?
(a, b + c), (b, c + a) and (c, a + b)
Find the area of triangle AGF
Using Heron’s formula, find the area of a triangle whose sides are 10 cm, 24 cm, 26 cm
If the side of a rhombus is 10 cm and one diagonal is 16 cm, the area of the rhombus is 96 cm2.
The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.
