Question

Find the coordinates of the point
divided which trisect the points
(1,-2) and (-3, 4)
3
Show Your Work​

Answer 1

$\;\;\underline{\textbf{\textsf{ Given:-}}}$

• The coordinates of the points are

(1 , -2) and (-3 , 4)

• A point trisect these given points divides into 3 equal parts.

$\;\;\underline{\textbf{\textsf{ To Find :-}}}$

• The coordinates of the points dividing the given lines.

$\;\;\underline{\textbf{\textsf{ Solution :-}}}$

Let us consider a point R(x , y) divides the line PQ into three equal parts ot trisect.

Then , the probable ratios will be 1:2 or 2:1

We know that,

$\boxed{ \tt{x = \frac{m x_{2} + n x_{1} }{m + n} \: \: , \: \: y = \frac{m y_{2} + n y_{1} }{m + n} }}$

$\underline{\:\textsf{ Taking ratio as 1:2 :}}$

$\sf x = \dfrac{1 \times ( - 3) + 2 \times 1}{1 + 2} \\ \\ \sf \longrightarrow x = \dfrac{ - 3+ 2}{3} \\ \\ \sf \longrightarrow x = \dfrac{ - 1}{3}$

_____★

$\sf y = \dfrac{1 \times (4) + 2 \times ( -2)}{1 + 2} \\ \\ \sf \longrightarrow y = \dfrac{4 - 4}{3} \\ \\ \sf \longrightarrow y = 0$

Therefore , the point (-1/3 , 0) trisect the line PQ

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$\underline{\:\textsf{Again, taking ratio as 2:1 :}}$

$\sf x = \dfrac{2 \times ( - 3) + 1 \times1}{1 +2} \\ \\ \sf \longrightarrow x = \dfrac{ - 6 + 1}{3} \\ \\ \sf \longrightarrow x = \dfrac{ - 5}{3}$

_____★

$\sf y = \dfrac{2\times (4) + 1\times (-2)}{1+2} \\\\ \sf \longrightarrow y = \dfrac{8 - 2}{3} \\\\ \sf \longrightarrow y = \dfrac{6}{3} \\\\ \sf\longrightarrow y = 2$

$\;\;\underline{\textbf{\textsf{ Hence-}}}$

$\underline{\textsf{ The other point trisect the line AB is \textbf{ (-5/3 , 2)}}}.$

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Answer 2

Answer:

Answer : (-5/3, 2)

Hope it right