Question

The points (2,3) and (4,1) are collinear with the point





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Answer 1

Answer:

Step-by-step explanation:

Given :

The points A (2,3) and B(4,1)

To find

The coordinates of a point C(x,y) which is co-linear with A and B

Solution:

If A,B and C are co-linear then

area of $\triangle$ ABC =0

⇒  $\frac12\times [ 2(1-y) +4(y-3) + x(3-1) ]=0$

⇒  2-2y+4y-12+2x=0

⇒  2x + 2y = 10

⇒  x+y=5

⇒ y=5-x------------------------(1)

We assume that point C is in quadrant I

and x,y are positive integers

then

x=0,1,2,3,4,5

and y=5,4,3,2,1,0

Answer:

Thus the possible coordinates of C are:

(0,5),(1,4),(2,3),(3,2),(4,1) and (5,0)

Formula used:

Area of a triangle

= $\frac12$ [(y1 + y2)(x1 – x2 ) + (y1 + y3 )(x3 – x1) – (y2 + y3 ) (x3 – x2 )]