Question

HOLA ,




$\huge \fbox \red{❥ Question}$


In which quadrant the point P that divides the line segment joining the points A(2, -5) and B(5,2) in the ratio 2 : 3 lies? ​

Answer 1

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⠀⠀⠀⠀⠀⠀${\huge{\mathcal{\red{❥MrStark}}}}$

$\huge\mathfrak{\color{red}{\underline{\underline{solutíón♡}}}}$

Given:

• Point P(x,y) Divides the join of A(2,–5) and B(5,2) in the ratio 2:3 .

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• To find → P lies on which Quadrant.

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Solution :

Formula to be used

If P(x,y) divides the join of A(a,b) and B(c,d)

in the ratio m:n

in the ratio M:N then,

Coordinates of P

$(x = \frac{m \times c + n \times a}{m + n} \ \:and \: y = \frac{m \times d + n \times b}{m + n} )$

Here,

• a = 2
• b = –5
• c = 5
• d = 2.

• Also, m = 2
• n = 3

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→ Coordinate of P =

$( x = \frac{2 \times 5 + 3 \times 2}{2 + 3} \: \: \: \: \: y = \frac{2 \times 2 + 3 \times (- 5)}{2 + 3})$

→$(x = \frac{10 + 6}{5} \: \: \: \: \: \: \: \: \: y = \frac{4 - 15}{5})$

→$(x = \frac{16}{5} \: \: \: \: y = \frac{ - 11}{5})$

Thus, The coordinates of point P is $p( x = \frac{16}{5} \: \: \: \: \: y = \frac{ - 11}{5} )$

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⠀Hence, the coordinate of P lies on 4th Quadrant.

Answer 2

Step-by-step explanation:

$⠀\Large\:{\bf{\dag}\:{\underline{\underline{\frak{Dinu\:}}}}} \\ \\ </p><p></p><p>Given: \\ </p><p></p><p>Point P(x,y) Divides the join of A(2,–5) and B(5,2) in the ratio 2:3 . \\ </p><p></p><p>━━━━━━━━━━━━━━ \\ </p><p></p><p>To find → P lies on which Quadrant. \\ </p><p></p><p>━━━━━━━━━━━━━ \\ </p><p></p><p>Solution : \\ </p><p></p><p>Formula to be used \\ </p><p>If P(x,y) divides the join of A(a,b) and B(c,d) \\ </p><p>in the ratio m:n \\ </p><p>in the ratio M:N then, \\ </p><p></p><p>Coordinates of P \\ </p><p></p><p>(x = \frac{m \times c + n \times a}{m + n} \ \:and \: y = \frac{m \times d + n \times b}{m + n} )(x=m+nm×c+n×a andy=m+nm×d+n×b) \\ </p><p></p><p>Here, \\ </p><p></p><p>a = 2 \\ </p><p></p><p>b = –5 \\ </p><p></p><p>c = 5 \\ </p><p></p><p>d = 2. \\ </p><p></p><p>Also, m = 2 \\ </p><p></p><p>n = 3 \\ </p><p></p><p>━━━━━━━━━━━━━ \\ </p><p>→ Coordinate of P = \\ </p><p>( x = \frac{2 \times 5 + 3 \times 2}{2 + 3} \: \: \: \: \: y = \frac{2 \times 2 + 3 \times (- 5)}{2 + 3})(x=2+32×5+3×2y=2+32×2+3×(−5)) \\ </p><p>→(x = \frac{10 + 6}{5} \: \: \: \: \: \: \: \: \: y = \frac{4 - 15}{5})(x=510+6y=54−15) \\ </p><p>→(x = \frac{16}{5} \: \: \: \: y = \frac{ - 11}{5})(x=516y=5−11) \\ </p><p></p><p>Thus, The coordinates of point P is p( x = \frac{16}{5} \: \: \: \: \: y = \frac{ - 11}{5} )\\ </p><p></p><p>━━━━━━━━━━━━━ \\ </p><p>⠀⠀⠀⠀⠀</p><p>⠀Hence, the coordinate of P lies on 4th Quadrant. \\ </p><p>$

$\large{ | | } \Large\:{\bf{\dag}\:{\underline{\underline{\frak{Dinu}}}}} |?|$