Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.
The perimeter of a triangle is 300 m. If its sides are in the ratio 3 : 5 : 7. Find the area of the triangle ?
The perimeter of a triangular field is 240 dm. If two of its sides are 78 dm and 50 dm, find the length of the perpendicular on the side of length 50 dm from the opposite vertex.
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.
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.
Sides of a triangle are cm 45 cm, 39 cm and 42 cm, find its area.
Look at the measures shown in the adjacent figure and find the area of ☐ PQRS.
Find the area of the triangle formed by the points
(1, – 1), (– 4, 6) and (– 3, – 5)
If the points A(– 3, 9), B(a, b) and C(4, – 5) are collinear and if a + b = 1, then find a and b
The perimeter of a triangle is 50 cm. One side of a triangle is 4 cm longer than the smaller side and the third side is 6 cm less than twice the smaller side. Find the area of the triangle.
