Question

Refer to Front View
Find the co-ordinates of the point which divides the line segment joining the points A
and B in the ratio 1:3 internally.
() (8.5.20)
(W) (2.0.9.5)
(1H) (3.0.7.5)
(20.8.5​

Answer 1

Correct Question :- Find the co-ordinates of the point which divides the line segment joining the points A(1, -3) and B(-3, 9) in the ratio 1 : 3 internally. ?

Solution :-

we know that, section formula says that, if R(x,y) divides P(a, b) and Q(c, d) in ratio m : n internally , than :-

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

Let us assume that, C(x , y) divides AB in the ration 1 : 3 internally .

then, we have given that,

• a = 1
• b = (-3)
• c = (-3)
• d = 9
• m = 1
• n = 3

putting all values in section formula now, we get,

→ x = (cm + an)/(m + n)

→ x = {(-3)*1 + 1*3} / (1 + 3)

→ x = (-3 + 3) / 4

→ x = 0 / 4

→ x = 0 .

and,

→ y = (dm + bn)/(m + n)

→ y = {9*1 + (-3)*3} / (1 + 3)

→ y = (9 - 9) / 4

→ y = 0 / 4

→ y = 0 .

Hence, origin (0,0) divides the line segment joining the points A(1, -3) and B(-3, 9) in the ratio 1 : 3 internally .

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