Question

if the point p (-1,2) divides the line segment joining a (2,5) and b in the ratio 3:4 then the coordinate of b are
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Answer 1

Step-by-step explanation:

this picture will absolutely help you!

Answer 2

The co - ordinates of B is (-5, -2).

If the point P(-1, 2) divides the line segment joining A(2, 5) and B in the ratio 3 : 4.

We have to find the co - ordinates of B.

Using section formula,

$(x,y)=\left(\frac{m_1x_2+m_2x_1}{m_1+m_2},\frac{m_1y_2+m_2y_1}{m_1+m_2}\right)$

Here, m₁ : m₂ = 3 : 4 , (x₁ , y₁) = (2, 5) , (x , y) = (-1, 2)

⇒(-1, 2) = [(3 × x₂ + 4 × 2)/(3 + 4), (3 × y₂ + 4 × 5)/(3 + 4)]

⇒(-1, 2) = [(3x₂ + 8)/7 , (3y₂ + 20)/7 ]

∴ -1 = (3x₂ + 8)/7 ⇒-7 = 3x₂ + 8

⇒x₂ = -5

and 2 = (3y₂ + 20)/7

⇒14 = 3y₂ + 20

⇒y₂ = -2

Therefore the co - ordinates of B is (-5, -2).