Advertisements
Advertisements
Question
The area of the triangle formed by (a, b + c), (b, c + a) and (c, a + b)
Options
a + b + c
abc
(a + b + c)2
0
Solution
We have three non-collinear points A ( a,b + c) ; B ( b, c + a) ; C( c,a + b).
In general if `A (x_1 ,y_1 ) ; B (x_2 , y_2 ) ; C (x_3 , y_3) ` are non-collinear points then are of the triangle formed is given by-
`"ar" (Δ ABC ) = 1/2|x_1 (y_2 - y_3) + x_2 (y_3 - y_1) +x_3 (y_1 - y_2 )|`
So,
`"ar" (Δ ABC) = 1/2 |a(c +a -a -b) + b(a + b-b-c) + c(b + c-c-a)|`
`= 1/2 [a(c-b)+b(a-c)+c(b-a)]`
= 0
APPEARS IN
RELATED QUESTIONS
Find a point on the x-axis which is equidistant from the points (7, 6) and (−3, 4).
Prove that the points (0, 0), (5, 5) and (-5, 5) are the vertices of a right isosceles triangle.
The points (3, -4) and (-6, 2) are the extremities of a diagonal of a parallelogram. If the third vertex is (-1, -3). Find the coordinates of the fourth vertex.
Show that the points A(2,1), B(5,2), C(6,4) and D(3,3) are the angular points of a parallelogram. Is this figure a rectangle?
In what ratio does y-axis divide the line segment joining the points (-4, 7) and (3, -7)?
If the points A (2,3), B (4,k ) and C (6,-3) are collinear, find the value of k.
Mark the correct alternative in each of the following:
The point of intersect of the coordinate axes is
Find the centroid of the triangle whose vertices is (−2, 3) (2, −1) (4, 0) .
If the vertices of a triangle are (1, −3), (4, p) and (−9, 7) and its area is 15 sq. units, find the value(s) of p.
Find the value of a for which the area of the triangle formed by the points A(a, 2a), B(−2, 6) and C(3, 1) is 10 square units.
If the centroid of the triangle formed by points P (a, b), Q(b, c) and R (c, a) is at the origin, what is the value of a + b + c?
Find the value of a so that the point (3, a) lies on the line represented by 2x − 3y + 5 = 0
The distance between the points (cos θ, 0) and (sin θ − cos θ) is
If points (t, 2t), (−2, 6) and (3, 1) are collinear, then t =
If the area of the triangle formed by the points (x, 2x), (−2, 6) and (3, 1) is 5 square units , then x =
The ratio in which the line segment joining points A (a1, b1) and B (a2, b2) is divided by y-axis is
Point (–3, 5) lies in the ______.
(–1, 7) is a point in the II quadrant.
Find the coordinates of the point whose ordinate is – 4 and which lies on y-axis.
The distance of the point (–4, 3) from y-axis is ______.
