Question

The locus of a point which is collinear with the points (3 4) and (-4 3) is

Answer 1

Answer:

Step-by-step explanation:

Let P(h,k) is a point which is collinear with points A(3,4) and B (-4,3).

Slope of PA=Slope of PB

(k-4)/(h-3)=(k-3)/(h+4)

(k-4)(h+4)=(k-3)(h-3)

kh+4k-4h-16=kh-3k-3h+9

7k-h=25.

Locus of P is:-

7y-x=25 , answer.

Answer 2

Thus, the locus of this two point is $7y-x=25$

Step-by-step explanation:

Given;

Point $A(3,4)$ and $B(-4,3)$

Let,

$P(x,y)$ is a point which is collinear  with point $A(3,4)$ and $B(-4,3)$

∴ Slope of $PA$$=$Slope of $PB$

⇒$\frac{4-y}{3-x} =\frac{3-y}{-4-x}$

⇒$-16-4x+4y+xy=9-3x-3y+xy$

⇒$-4x+3x+4y+3y=9+16$

⇒$7y-x=25$

∴ The locus of this two point is $7y-x=25$