show that (4,3) (5,1) (1,9) are collinear
Answers
Answer:
your answer
Step-by-step explanation:
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)(x
1
=4,y
1
=3),(x
2
=5,y
2
=1) and (x_{3}=1, y_{3}=9)(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})=0x
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)=04(1−9)+5(9−3)+1(3−1)=0
⇒ 4 (-8)+5 (6)+1 (2)=04(−8)+5(6)+1(2)=0
⇒ -32+30+2=0−32+30+2=0
⇒ -32+32=0−32+32=0
⇒ 0=00=0 , proved.
Hence, the points (4,3), (5,1) and (1,9) are collinear, proved.
hope this helps
Answer:
bs kro yarr itna Mat pdo pagal ho jao ge