The coordinates of A ,B ,C are (6,3),(-3...

The coordinates of `A ,B ,C` are `(6,3),(-3,5),(4,-2)` , respectively, and `P` is any point `(x ,y)` . Show that the ratio of the area of ` P B C` to that of ` A B C` is `(|x+y-2|)/7dot`

Text Solution

AI Generated Solution

Topper's Solved these Questions

COMPLEX NUMBERS AND QUADRATIC EQUATIONS
CENGAGE ENGLISH|Exercise All Questions|886 Videos
DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS
CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

The coordinates of A ,\ B ,\ C are (6,\ 3),\ (-3,\ 5) and (4,\ -2) respectively and P is any point (x ,\ y) . Show that the ratio of the areas of triangles P B C and A B C is |(x+y-2)/7| .

The coordinates of points A, B, C and P are (6, 3), (-3, 5), (4, -2) and (x, y) respectively, prove that (DeltaPBC)/ (Delta ABC) = (x+y-2)/7

If the coordinates of two points A and B are (3, 4) and (5,-2) , respectively, find the coordinates of any point P if P A=P Bdot Area of P A B is 10 sq. units.

If the coordinates of two points A and B are (3,\ 4) and (5,\ -2) respectively. Find the coordinates of any point P , if PA = PB, and area of triangle PAB is 10.

The coordinates of points A,B,C and D are (-3, 5), (4, -2), (x, 3x) and (6, 3) respectively and Area of (Delta ABC)/(Delta BCD)=(2)/(3) ,find x.

If A(6, 3), B(3, 5), C(4, 2), P (alpha, beta) , then the ratio of the areas of the triangles PBC, ABC is

In A B C , P divides the side A B such that A P : P B=1:2 . Q is a point in A C such that P Q B C . Find the ratio of the areas of A P Q and trapezium B P Q C .

A plane meets the coordinate axes in A ,B ,C such that the centroid of triangle A B C is the point (p ,q ,r)dot Show that the equation of the plane is x/p+y/q+z/r=3.

CENGAGE ENGLISH-CONIC SECTIONS-All Questions

If the points (x1, y1),(x2,y2), and (x3, y3) are collinear show that...
Text Solution
|
Find dy/dx, if y = (1 - tan^2x)/(1 + tan^2x) .
Text Solution
|
The coordinates of A ,B ,C are (6,3),(-3,5),(4,-2) , respectively, and...
Text Solution
|
A line cuts the x-axis at A (7, 0) and the y-axis at B(0, - 5) A varia...
Text Solution
|
For points P-=(x1, y1) and Q-=(x2, y2) of the coordinate plane, a new ...
Text Solution
|
Statement 1 : Let the vertices of a A B C be A(-5,-2),B(7,6), and C(5...
Text Solution
|
If (x , y) and (x ,y) are the coordinates of the same point referred t...
Text Solution
|
O X and O Y are two coordinate axes. On O Y a fixed point P(0,c) is t...
Text Solution
|
Two vertices of a triangle are (5,-1) and (-2,3) If the orthocentre of...
Text Solution
|
The vertices of a triangle are [a t1t2,a(t1 +t2)], [a t2t3,a(t2 +t3)],...
Text Solution
|
If (-6,-4),(3,5),(-2,1) are the vertices of a parallelogram, then the...
Text Solution
|
The maximum area of the triangle whose sides a,b and c satisfy 0leqale...
Text Solution
|
If (-4,0) and (1,-1) are two vertices of a triangle of area 4s qdotu n...
Text Solution
|
Let O-=(0,0),A-=(0,4),B-=(6,0)dot Let P be a moving point such that th...
Text Solution
|
Through the point P(alpha,beta) , where alphabeta>0, the straight line...
Text Solution
|
The vertices A and D of square A B C D lie on the positive sides of x ...
Text Solution
|
A light ray emerging from the point source placed at P(2,3) is reflect...
Text Solution
|
If the origin is shifted to the point ((a b)/(a-b),0) without rotation...
Text Solution
|
In A B C , the coordinates of B are (0,0),A B=2,/A B C=pi/3, and t...
Text Solution
|
If a triangle A B C ,A-=(1,10), circumcenter -=(-1/3,2/3), and orthoce...
Text Solution
|