Question

using the distance formula, show that the points A (-6,0) ; B(0,5) ; C(6,10) are collinear.

Answer 1

hope this helps you........

Answer 2

Answer:

So , the given points  A (-6,0) ,B (0,5) and C (6, 10 ) are collinear .

Step-by-step explanation:

Explanation:

Given  points are , A (-6,0) ,B (0,5) and C (6, 10 )

As we know the distance formula = $\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }$

Condition for a collinear ;

If the sum of distance  between (AB + BC = AC) than  we say that the given points are  collinear .

Step 1:

By distance formula  AB = $\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }$

AB =  $\sqrt{(0 - (-6) )^{2} +(5 - 0 )^{2} }$

⇒AB = $\sqrt{36 + 25 } = \sqrt{61}$

And we have B (0,5) and (6,10)

BC = $\sqrt{(6- 0 )^{2} +(10-5 )^{2} }$

BC = $\sqrt{36 + 25 } = \sqrt{61}$

Similarly ,  by distance formula AC = $\sqrt{(6 - (-6) )^{2} +(10- 0 )^{2} }$

AC = $\sqrt{(12 )^{2} +(10 )^{2} }$ = $\sqrt{144 + 100 } = \sqrt{244}$

⇒AC = $2\sqrt{61}$

Now , we  check whether it is collinear or not ,

∴ AB + BC = AC  

put the value of AB , BC and AC in the above equation

⇒$\sqrt{61}+ \sqrt{61} = 2\sqrt{61}$

⇒$2\sqrt{61} = 2\sqrt{61}$

Final answer :

Hence , the given points are collinear .

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