Question

Question ☟

What Is Internal Division Formula?
__________________________

Also Derive Internal Division Formula?
__________________________
NOTE ☟
☞ Full Explanation.
☞ Irreverent Answer RePorted.
​

Answer 1

Answer:

1. P={[(mx2+nx1)/(m+n)],[(my2+ny1)/(m+n)]}

2. Now using the formula C(x, y) = { (m × x2 + n × x1) / (m + n ) , (m × y2 + n × y1) / (m + n ) } as C is dividing internally.

EASY UNDERSTANDING THERE IS AN IMAGE

I HOPE YOU HAVE UNDERSTAND MATE AND I HOPE IT WAS HEPLFUL TO YOU MATE

Answer 2

What Is Internal Division Formula?

$\sf\pink{Answer.. }$

Coordinates of the point P(x , y) which divides the line segment joining the points A (X₁ , Y₁ ) and B(X₂ Y₂) internally in the ratio m₁ : m₂

${\bold{\green{\underline{\underline{Derivation \: of \: Internal \: Division \: Formula \: ....}}}}}$

In ∆PRS & ∆RQT

__________________

$⟼ \frac{PR}{RQ} = \frac{PS}{RT} = \frac{SR}{QT}$

$⇒ \frac{m}{n} = \frac{x - x1}{x2 - x} = \frac{y - y1}{y2 - y}$

$\sf\blue{ Equating..}$

$\frac{m}{n} = \frac{x - x1}{x2 - x}$

⟼ m x₂ − mx = nx − n x₁

⟼ m x₂ + n x₁ = mx + nx

⟼ m x₂ + n x₁ = n ( m + n )

⟼

$\;\large{\boxed{\bf{\red{x = \frac{mx2 + nx1}{m + n} }}}}$

$\sf\blue{ Equating..}$

$\frac{m}{n \: } = \frac{y - y1}{y2 - y}$

⟼ my₂ − my = ny − ny₁

⟼ my₂ + ny₁ = my + ny

⟼ my₂ + ny₁ = ʏ (m + n)

⟼

$\;\large{\boxed{\bf{\red{y = \frac{my2 + ny1}{m + n} }}}}$

____________◆◇◆◇◆◇◆◇_______________

$\sf\blue{hope \: this \: helps \: you!! \: }$

Happy Learning ;)

@Mahor2111