Question

If the line joining the points ( -1 , 3 ) and ( 4 , -3 ) pass through the point ( a , b ) then prove that a + b = 2.

Answer 1

To Prove :

a + b = 2.

SolutioN :

Let,

• Point A( - 1 , 3 )
• Point B( 4 , - 2 )
• Point P( a , b )

☛ Condition.

• According to let Point A and B are join to form a line and Point P passes through it.

Now,

We have Formula ( Area )

$\tt \dagger \: \: \: \: \: \dfrac{1}{2}\Big[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\Big]$

Where as,

• x1 = - 1.
• x2 = 4.
• x3 = a.
• y1 = 3.
• y2 = - 2.
• y3 = b.

✎ Putting given Value in Formula.

$\tt : \implies \dfrac{1}{2}\Big[ - 1( - 2 - b)+4(b - 3)+a(3 + 2)\Big]$

$\tt : \implies 0= \dfrac{1}{2}\Big[ 2 + b+4b - 12+3a + 2a\Big]$

$\tt : \implies 0= \Big[ 5a + 5b - 10\Big]$

$\tt : \implies 5a + 5b = 10.$

$\tt : \implies 5(a + b) = 10.$

$\tt : \implies a + b= 2.$

¶Hence Proved.