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
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
The perimeter of a triangle is 300 m. If its sides are in the ratio 3 : 5 : 7. Find the area of the triangle ?
A rhombus sheet, whose perimeter is 32 m and whose one diagonal is 10 m long, is painted on both sides at the rate of Rs 5 per m2. Find the cost of painting.
A hand fan is made by stitching lo equal size triangular strips of two different types of paper as shown in Fig. 12.28. The dimensions of equal strips are 25 cm, 25 cm and 14 cm. Find the area of each type of paper needed to make the hand fan.
Find the area of a triangle whose sides are 3 cm, 4 cm and 5 cm respectively.
Find the area of the triangle formed by the points
(1, – 1), (– 4, 6) and (– 3, – 5)
Determine whether the sets of points are collinear?
(a, b + c), (b, c + a) and (c, a + b)
The area of triangle formed by the points (− 5, 0), (0, – 5) and (5, 0) is
The cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of Rs 3 per m2 is Rs 918.
A field in the form of a parallelogram has sides 60 m and 40 m and one of its diagonals is 80 m long. Find the area of the parallelogram.
