Question

Hii....

show that the points ( 1,1) , (5,2) and (9,5) are collinear.

No spamming...

Answer 1

_____Heyy Buddy ❤_____

_____Here's your Answer _____

Let A( 1, -1) , B( 5,2) and C ( 9,5) be the points.

So, By the formula

$\sqrt{ {(x2 - x1)}^{2} } + { (y2 - y1) }^{2}$
NOW,

AB =
$\sqrt{ {(5 - 1)}^{2} } + \sqrt{{(2 + 1)}^{2}}$

$\sqrt{16 + 9}$

$\sqrt{25}$

=>AB = 5.

BC =
$\sqrt{ {(5 - 9)}^{2} + { (2 - 5)}^{2} }$

$\sqrt{16 + 9}$

$\sqrt{25}$

=> BC = 5.

And AC =
$\sqrt{ {(1 - 9)}^{2} + {( - 1 - 5)}^{2} }$

$\sqrt{64 + 36}$

$\sqrt{100}$

=> AC = 10.

Now,

AC = AB + BC.

AC is the straight line B is the mid point of the line.

Hence,

A, B and C are collinear points.
✔✔✔

Answer 2

$\huge\bf\green {Hey \: there!}$



▶ To Prove :



( 1 , - 1 ) , ( 5 , 2 ) , ( 9 , 5 ) are collinear




▶ Explanation :




Three points are collinear if :



$\mathsf {x_1( y_2 - y_3 ) + x_2 ( y_3 - y_1 ) + x_3 ( y_1 - y_2 ) = 0}$




Here :



$\mathsf {x_1 = 1 , x_2 = 5 , x_3 = 9 }$


$\mathsf {y_1 = - 1, y_2 = 2, y_3 = 5}$




LHS = [1 ( 2 - 5 )] + 5 [( 5 - ( - 1 )] + 9 [( - 1 ) - 2]



= [( 1 × ( - 3 )] + [( 5 × 6 )] + [( 9 × ( - 3 )]



= - 3 + 30 - 27


= - 30 + 30


= 0




RHS = 0



LHS = RHS



✔✔ Hence, it is proved ✅✅





$\mathbb {\huge {\fcolorbox{yellow}{green}{Hope It Helps}}}$




$\huge\bf\purple {\#BeBrainly}$