Question

find the coordinates of the points which divides the join of (-1,7) and (4-3) in the ratio 2:3​

Answer 1

Answer :-

$\rm P = (1, 3)$

Given :-

• The point A (-1, 7) and point B (4, 3) divides the point P in ratio 2:3

To find :-

• The co-ordinates of p

Solution :-

As we know that ,

If a point A $\rm (x_1,y_1)$ and point B $\rm (x_2,y_2)$ divides the line segment point P in ratio m:n then the co-ordinates of P are

$\rm P = \bigg(\cfrac{mx_2+nx_1}{m+n } , \dfrac{my_2+ny_1}{m+n} \bigg)$

Nothing but this is called as Section - formula Internal division

If we substitute the values then we get the co-ordinates of P

$\rm (x_1,y_1)= (-1 , 7)\rm (x_2,y_2) =(4, -3) \rm m:n = 2:3$

Substituting the values ,

$\rm P = \bigg(\cfrac{mx_2+nx_1}{m+n } , \dfrac{my_2+ny_1}{m+n} \bigg)$

$\rm P = \bigg(\cfrac{2(4) +3(-1)}{2+3} , \dfrac{2(-3)+3(7)}{2+3} \bigg)$

$\rm P = \bigg(\cfrac{8 -3}{5} , \dfrac{-6+21}{5} \bigg)$

$\rm P = \bigg(\cfrac{5}{5} , \dfrac{15}{5} \bigg)$

$\rm\red{P = (1, 3)}$

So, the coordinates of the points which divides the join of (-1,7) and (4-3) in the ratio 2:3 is P = (1 ,3 )

Note:-

For  easy understanding here I have named the points with Alphabets.

Know more similar question in brainly :-

https://brainly.in/question/41658750

Answer 2

αnѕwєr

(x1,y1) is (-1,7)

(x2,y2) is (4,-3)

m1=2

m2=3

x = m1x2+m2x1/m1+m2

= (2×4)+(3×-1)/(2+3) = (8-3)/5

= 5/5 = 1

y = m1y2+m2y1/m1+m2

= (2×-3)+(3×7)/(2+3) = (-6+21)/5

= 15/5 = 3

So, the point is (1,3)

hope it helps