Question

find the relation between x and y if the points A(x, y), B(-5,7) and c(-4,5) are colinear​

Answer 1

Answer:

$\bold\red{2x+y+3=0}$

Step-by-step explanation:

Given,

A (x,y) , B (-5,7) and C (-4,5) are collinear

Therefore,

the area of triangle ABC must be zero.

Thus,

we get,

$= > \frac{1}{2} |x(7 - 5) - y( - 5 + 4) + 1( - 25 + 28)| = 0 \\ \\ = > |2x + y + 3| = 0 \\ \\ = > 2x + y + 3 = 0$

Answer 2

Since A,B and C are colinear,

Slope of AB= Slope of BC

Slope of BC=

$\frac{y2 - y1 }{x2 - x1}$

$= \frac{5 - 7}{ - 4 - ( - 5)}$

$= - 2$

Slope of AB= -2

$\frac{y2 - y1}{x2 - x1} = - 2$

$\frac{7 - y}{ - 5 -x } = - 2$

$7 - y = 10 + 2x$

$2x + y = - 3$