Math, asked by mammastan70, 9 months ago

find the points of trisection of
joining A (2,-3), B (4,5
line

Answers

Answered by Anonymous

$\huge{\underline{\bf{\blue{Question:-}}}}$

find the points of trisection of joining A (2,-3), B (4,5) line.

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$\large{\underline{\bf{\pink{Answer:-}}}}$

p(8/3,-1/3)

Q(10/3,7/3)

$\large{\underline{\bf{\purple{Explanation:-}}}}$

$\large{\underline{\bf{\green{Given:-}}}}$

Two points are given as A(2, -3) and B(4,5).

$\large{\underline{\bf{\green{To\:Find:-}}}}$

We need to find the points of trisection.

$\huge{\underline{\bf{\red{Solution:-}}}}$

______________________________

A(2,-3)⠀⠀⠀p⠀⠀⠀⠀⠀Q⠀⠀⠀⠀⠀B(4,5)

Let p and Q divides the line segment AB.

P divides AB in the ratio:- 1:2

and Q divides AB in the ratio :- 2:1

The points are as

AP = 1

PQ = 1

QB = 1

by using section formula

$\bf{\underline{\boxed{\frac{m_1x_2+m_2x_1}{m_1+m_2}, \frac{m_1y_2+m_2y_1}{m_1+m_2}}}}$

p divides the line segment in 1:2

m 1=1⠀⠀⠀⠀⠀m 2 =2

A(2,-3), B(4,5)

x 1 = 2⠀⠀⠀⠀⠀x2=4

y 1 = -3⠀⠀⠀⠀⠀y2 = 5

$\bf\:Q(\frac{1\times4+2\times2}{1+2},\frac{1\times5+2\times-3}{1+2})$

$:\implies\bf\:p(\frac{4+4}{3},\frac{5-6}{3})$

$:\implies\bf\:p(\frac{8}{3},\frac{-1}{3})$

Now Q divides the line segment in the ratio 2:1.

m 1 = 2⠀⠀⠀⠀⠀m 2 = 1

$\bf\\:Q(\frac{2\times4+1\times2}{1+2},\frac{2\times5+1\times-3}{1+2})$

$:\implies\bf\:Q(\frac{8+2}{3},\frac{10-3}{3})$

$:\implies\bf\:Q(\frac{10}{3},\frac{7}{3})$

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Answered by HrGabru0001

Answer:

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find the points of trisection of
joining A (2,-3), B (4,5
line