Question

Using distance formula decide whether the
points (4,3), (5, 1) and (1,9) are collinear not? please answer ​

Answer 1

Answer:

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.

Name Arushi Class 7 B