Question

If the points P(-3,9),Q(a,b), R(4,-5)are collinear and a+b=1 .find the value of a & b

Answer 1

Let the given 3 points be A(1,X),B(5,2),C(9,5)

Consider ‘B' Let (x1=5,y1=2)

Similarly for A & C (x3=1,y3=X) & (x2=9,y2=5) respectively.

Lets recall the the slope point form of straight line (y-y1)=m(x-x1)

Where ‘m’ is slope which is equal to (y2-y1)/(x2-x1)

In this question m=5–2/9–5 =3/4.

Now using slope point form:

y-2=(x-5)3/4 = 4y-8=3x-15

=> 3x-4y-7=0 (this the equation of line)

Now if we put the value of ‘x' co -oridinate then we must get the value of ‘y' co oridinate

Put point A(1,X)

3–4X-7=0

=> -4X=4

X= -1

Method 2:-

For collinear all three point must lie on same line and the slope will be equal for each and every point.

i.e.

(y2-y1)/(x2-x1) = (y3-y2)/(x3-x1)

(5–2)/(9–5) =(X-5)/(1–9)

-6=X-5

X=-1

If u get any problems comment and feel free to ask any other questions. Hope this will help you.

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Abhishek Kaushik, Childhood hobby, adulthood addiction

Answered Mar 9, 2017

All points lie in same line then it's slope will be equal I.e slope( 2–x/5–1)=slope (5–2/9–5)

Solving we get values of x=-1. Another method here all the points lie in same line so it's determinant should be zero ,I.e area of TRIANGLE should be zero.

Taking all the points in determinant and solve.

I hope it helps

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Khaja Musab Manzoor, M Tech Computer Aided Structural Engineering, International Institute of Information Technology, Hyderabad ...

Answered Mar 9, 2017

Ans : x = -1

Solution :

We have many different methods to find collinearity of the given three points. Few of them are

Slopes will be equal.

Area formed by that three points ( triangle) would be zero.

Determinent is equal to zero.

Let the given three points be

(a,b), (c,d), (e,f)

Slopes :

(f - d) /(e-c) = (d-b)/(c-a)

Area :

(1/2) × | a (d-f) + c (f-b) + e (b-d)| = 0

Determinent :

| a (d-f) + c (f-b) + e (b-d)| = 0

Let us consider 1st method (slope)

(5-2)/(9-5) = (2- x)/(5-1)

3/4 = (2-x)/4

(3/4) × 4 = 2-x

3 = 2 - x

x = 2-3

x = -1

☆ x = -1

In the similar way we can calculate the value of x by using the other two methods.

 · 

Answer 2

The pic might help you ^^