Question

Find the coordinates of the points which divides the join of X (-1, 7) and Y (4, -3) in the ratio 7 : 2.

Answer 1

Answer:

(x,y) = (26/9 , -7/9)

Step-by-step explanation:

Let the required point be (x,y)

The line joining the points (x₁,y₁) and (x₂,y₂) is divided in the ratio m:n

So, the coordinates of the point dividing the line in that ratio is:

(x,y) = (mx₂+nx₁/m+n , my₂+ny₁/m+n)

(x,y) = (7*4+2*-1 / 7+2 , 7*-3+2*7 / 7+2)

(x,y) = (28-2/9 , -21+14/9)

(x,y) = (26/9 , -7/9)

Hence, the coordinates of the points which divides the join of X (-1, 7) and Y (4, -3) in the ratio 7 : 2 is (26/9,-7/9).

I hope my answer helped you.

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Answer 2

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

Find the coordinates of the points which divides the join of X (-1, 7) and Y (4, -3) in the ratio 7 : 2.

$\bf\huge\blue{\underline{\underline{ Solution : }}}$

★ Given that,

• The coordinates of the points which divides the join of X (-1, 7) and Y (4, -3) in the ratio 7 : 2.

★ To find,

• Coordinates of the point which divides the line segment.

★ Formula :

By using Section Formula :-

$\boxed{\rm{\red{ Section\:Formula = \Bigg(\cfrac{m_{1}x_{2} + m_{2}x_{1}}{m_{1} + m_{2}} , \cfrac{m_{1}y_{2} + m_{2}y_{1}}{m_{1} + m_{2}} \Bigg) }}}$

★ Let,

• x1 = - 1 ; y1 = 7
• x2 = 4 ; y2 = - 3
• m1 = 7 ; m2 = 2

$\sf \implies XY = \Bigg( \cfrac{7(4)+2(-1)}{7+2},\cfrac{7(-3)+2(7)}{7+2} \Bigg)$

$\sf \implies XY =\Bigg(\cfrac{28 - 2}{9},\cfrac{-21 + 14}{9} \Bigg)$

$\sf \implies XY =\Bigg(\cfrac{26}{9},\cfrac{-7}{9} \Bigg)$

$\underline{\boxed{\rm{\purple{\therefore The\:Point\:which\:divides\:the\:line\:segment : XY = \Bigg(\cfrac{26}{9},\cfrac{-7}{9} \Bigg).}}}}\:\orange{\bigstar}$