Question

find the relation between P and Q if (1, 3)(0, 2) and( P, Q) are collinear​

Answer 1

Answer:

p(1,3), Q(0,2)

by distance formula

(P, Q) =√(x2-x1) 2 + ( y2-y1) 2 )

= √(0-1)2 +(2-3)2

=√1+1

=√2

therefor (P, Q) are collinear

Answer 2

The relation between P and Q is equal to "3P - Q = 4".

Explanation:

Given,

The three points (1, 3), (0, 2) and ( P, Q) are collinear​.

To find, the relation between P and Q = ?

The condition of three points are collinear​.

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

The three points (1, 3), (0, 2) and ( P, Q) are collinear​.

∴ $1(2-Q)+0(Q-3)+P(3-2)=0$

⇒ $2-Q+0+3P-6=0$

⇒ $-Q+3P-4=0$

⇒ 3P - Q = 4

∴ The relation between P and Q: 3P - Q = 4

Thus, the relation between P and Q is equal to "3P - Q = 4".