Advertisements
Advertisements
Question
Determine whether the sets of points are collinear?
`(-1/2, 3), (-5, 6) and (-8, 8)`
Advertisements
Solution
Let the points be `"A"(-1/2, 3), "B" (-5, 6) and "C"(-8, 8)`
Area of ∆ABC = `1/2[(x_1y_2 + x_2y_3+ x_3y_1) - (x_2y_1 + x_3y_3 + x_1y_3)]`
= `1/2[(-3 - 40 - 24) - (-15 - 48 - 4)]`
=`1/2[-67 + 67]`
= `1/2 xx 0`
= 0
Area of a ∆ is 0.
∴ The three points are collinear.
APPEARS IN
RELATED QUESTIONS
The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122m, 22m, and 120m (see the given figure). The advertisements yield an earning of ₹ 5000 per m2 per year. A company hired one of its walls for 3 months. How much rent did it pay?
Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540 cm. Find its area.
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 the shaded region in the given figure.
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.
Look at the measures shown in the adjacent figure and find the area of ☐ PQRS.
Find the area of triangle FED
The semi-perimeter of a triangle having sides 15 cm, 20 cm and 25 cm is
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.
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.
