Question

find the coordinates of the points of trisection of the line segment joining (4,-1) and-2,-3)​

Answer 1

Answer:

Step-by-step explanation:

if 13 cos theta = 5 find the value of  cosec theta

Answer 2

G I V E N :

• Endpoints of a segment are (4,-1) and (-2,-3).

T O F I N D :

• The points of trisection of the segment.

A N S W E R :

Let the given points be A (4, – 1) and B(- 2, - 3).

Let P and Q be the point of trisection. Therefore, we have :

• AP = PQ = QB

Trisection means is to divide a line segment into three equal parts. Hence, we can say that P divides AB in the ratio of 1:2 and Q divides in 2:1 .

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☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$\underline{\frak{Thus,\: coordinate \: of \: \textsf{\textbf{P}}\: is \: given \: by :}}$

$:\implies\sf P = \Bigg\lgroup \dfrac{mx_2 + nx_1}{m + n}, \dfrac{my_2 + ny_1}{m + n}\Bigg\rgroup$

$:\implies\sf P = \Bigg\lgroup \dfrac{1 \times ( - 2) + 2 \times 4}{1 + 2}, \dfrac{1 \times ( - 3) + 2 \times ( - 1)}{1 + 2}\Bigg\rgroup$

$:\implies\sf P = \Bigg\lgroup \dfrac{ - 2+ 8}{3}, \dfrac{- 3 - 2}{3}\Bigg\rgroup$

$:\implies\sf P = \Bigg\lgroup \dfrac{6}{3}, \dfrac{- 5}{3}\Bigg\rgroup$

$:\implies\sf P = \Bigg\lgroup 2, \dfrac{- 5}{3}\Bigg\rgroup$

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$\underline{\frak{Similarly\: the\: coordinate \: of \: \textsf{\textbf{Q}}\: is \: given \: by :}}$

$:\implies\sf Q = \Bigg\lgroup \dfrac{2 \times ( - 2) + 1 \times 4}{2 + 1}, \dfrac{2 \times ( - 3) + 1 \times ( - 1)}{2 + 1}\Bigg\rgroup$

$:\implies\sf Q = \Bigg\lgroup \dfrac{ - 4+ 4}{3}, \dfrac{ - 6 - 1}{3}\Bigg\rgroup$

$:\implies\sf Q = \Bigg\lgroup 0, \dfrac{ - 7}{3}\Bigg\rgroup$

Therefore, the coordinates of the point of trisection are :

$\bullet \: \: \underline{ \boxed{ \sf\Bigg\lgroup 2, \dfrac{- 5}{3}\Bigg\rgroup \: and \: \Bigg\lgroup 0, \dfrac{ - 7}{3}\Bigg\rgroup}}$

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