Question

In what ratio does the point C(3/5, 11/5) divide
the line segment joining the points A(3,5)
and B(-3,-2)?
​

Answer 1

Answer:

If any point (x, y) divides the line joining points (x1,y1) and (x2, y2) in the ratio m : n then,

x= (mx2+nx1)/(m+n)

y= (my2+ny1)/(m+n)

Here, x= 3/5 and y= 11/5

x1= 3; y1= 5; x2= -3; y2= -2

3/5 =(-3m+3n)/(m+n)

m+n=(-3m+3n)/(3/5)—-(1)

11/5=(-2m+5n)/(m+n)

m+n = (-2m+5n)/(11/5) —-(2)

From (1) and (2)

(-3m+3n)/(3/5) = (-2m+5n)/(11/5)

3m=2n

m/n = 2/3

Ans: Point C divides the line 2:3 ratio

Answer 2

Solution :-

section formula says that, if C(x,y) divides A(a, b) and B(c, d) in ratio m : n , than :-

• C(x , y) = (cm + an)/(m + n) , (dm + bn)/(m + n) .

given that,

• C(x ,y) = C(3/5, 11/5)
• A(a, b) = A(3, 5)
• B(c, d) = B(-3 , -2)

Let us assume that, C divided A and B in the ratio m : n .

then, putting given values we get,

→ x = (cm + an)/(m + n)

→ 3/5 = [(-3)m + 3n]/(m + n)

→ 3(m + n) = 5(-3m + 3n)

→ 3m + 3n = -15m + 15n

→ 3m + 15m = 15n - 3n

→ 18m = 12n

→ m/n = 12/18

→ m/n = 2/3

→ m : n = 2 : 3 (Ans.)

also, putting these values to verify y coordinates of C ,

→ y = (dm + bn)/(m + n)

→ 11/5 = [(-2) * 2 + 5 * 3] / (2 + 3)

→ 11/5 = (-4 + 15)/5

→ 11/5 = 11/5 (verify)

Therefore, the required ratio is equal to 2 : 3 .

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