Math, asked by vinaya7279, 1 year ago

Using the distance formula show that The points (4,3) (5,1) and (1,9) are collinear

Answers

Answered by nitthesh7
46
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Answered by harendrachoubay
19

The points (4,3), (5,1) and (1,9) are collinear, proved.

Step-by-step explanation:

Given,

(x_{1}=4, y_{1}=3), (x_{2}=5,y_{2}=1)and (x_{3}=1, y_{3}=9)

Prove that, the points (4,3), (5,1) and (1,9) are collinear.

If three points are collinear, then

Area of triangle is zero(0).

x_{1} (y_{2} -y_{3})+x_{2} (y_{3} -y_{1})+x_{3} (y_{1} -y_{2})=0

4 (1 -9)+5 (9 -3)+1 (3 -1)=0

4 (-8)+5 (6)+1 (2)=0

-32+30+2=0

-32+32=0

0=0, proved.

Hence, the points (4,3), (5,1) and (1,9) are collinear, proved.

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