Question

find the ratio in which the point (x,1) divides the line segment joining the points (-3,5)and(2,-5). also find the value of x

Answer 1

If the point P(X,y) divides the line having two ends points as (X1,y1) (X2,y2) in M1:M2 ratio then

P(X,y)= ((M2 X1 + M1 X2)/M1+M2. , (M2 y1+ m1y2)/M1+M2)

Given P(X,1) and two points (-3,5) and (2,-5)

P(X,1) = ((M2 (-3) + M1 (2))/M1+M2, (M2 (5)+M1 ( -5))/M1+M2)

Equate y coordinate to 1

So

5m2 -5m1 = M1+M2

4m2 = 6m1

M2/M1 = 6/4

= 3/2

M1/m2 = 2/3

M1:M2 = 2:3

Now substitute these values In X coordinate

X= (-3m2 + 2m1)/M1+M2

M1= 2 M2= 3

X = (-3*3+2*2)/2+3

= (-9+4)/5

= 5/5

= 1

So X=1