Question

Find the ratio in which the point (x,2) divide the line segment joining the point (-3,-4) and (3,5) also find the value of x​

Answer 1

Answer:

Let the line x−y−2=0 divide the line segment AB at point C(x,y) in the ratio m:n.

By section formula,

C(x,y)=[

m+n

m×8+n×3

,

m+n

m×9+n×−1

]

C(x,y)=[

m+n

8m+3n

,

m+n

9m−n

]

Since, point C lie on the line x−y−2=0,

m+n

8m+3n

−

m+n

9m−n

−2=0

8m+3n−9m+n−2m−2n=0

3m=2n

n

m

=

3

2

Hence, the required ratio is 2:3.

Step-by-step explanation:

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Answer 2

Answer :-

Ratio is 2 : 1.

Value of x is 1.

Step-by-step explanation :-

∅ Let the point (x,2) divide the line in k : 1 ratio.

∅ Coordinates : (Section formula)

⇒ x = (3k -3)/(k+1)

⇒ 2 = (5K -4)/(k+1)

2(k+1) = 5k - 4

2k + 2 = 5k - 4

k = 6/3

k = 2/1

∴ The ratio is 2 : 1.

∅ Substitute k value in x = (3k -3)/(k+1) :

x = (3×2-3)/(2+1)

x = (6-3)/3

x = 3/3

x = 1

∴ Value of x is 1.