Advertisements
Advertisements
प्रश्न
Show that the following points are collinear:
(i) A(2,-2), B(-3, 8) and C(-1, 4)
उत्तर
`"Let " A(x_1=2,y_1=-2) B (x_2=-3, y_2=8) and C(x_3=-1,y_3=4)` be the given points.
`No w , x_1 (y_1-y)3)+x_2(y_3-y_1) + x_3(y_1-y_2)`
=2(8-4)+(-3)(4+2)+(-1)(-2-8)
=8-18+10
=0
Hence, the given points are collinear.
APPEARS IN
संबंधित प्रश्न
If D, E and F are the mid-points of sides BC, CA and AB respectively of a ∆ABC, then using coordinate geometry prove that Area of ∆DEF = `\frac { 1 }{ 4 } "(Area of ∆ABC)"`
Find the area of the quadrilateral whose vertices, taken in order, are (-4, -2), (-3, -5), (3, -2) and (2, 3).
If A(–5, 7), B(–4, –5), C(–1, –6) and D(4, 5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD
Find the centroid of ΔABC whose vertices are A(-1, 0) B(5, -2) and C(8,2)
Find the area of ΔABC whose vertices are:
A(10,-6) , B (2,5) and C(-1,-3)
For what value of k(k>0) is the area of the triangle with vertices (-2, 5), (k, -4) and (2k+1, 10) equal to 53 square units?
If the points A (x, y), B (3, 6) and C (−3, 4) are collinear, show that x − 3y + 15 = 0.
In ☐ABCD, l(AB) = 13 cm, l(DC) = 9 cm, l(AD) = 8 cm, find the area of ☐ABCD.
The area of a triangle with vertices (–3, 0), (3, 0) and (0, k) is 9 sq.units. The value of k will be ______.
Triangles having the same base have equal area.