Question

the point of A (-1,-7) and B(4,-3) and of the line AB-point P divides in Ratio 2:3 find the coordinate of point P.​

Answer 1

Answer :-

• (1, -27/5)

Topic :-

• Co-ordinate Geometry

Given :-

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

To find :-

• Co-ordinates of p

Requird concept :-

If the point A= ${(x_1,y_1)}$ and point B =${(x_2,y_2)}$ divides the point p in ratio m:n then the co-ordinates of P are

$p = \bigg( \dfrac{mx_2 + nx_1}{m + n} \dfrac{my_2 + ny_1}{m + n} \bigg)$

i.e this formula is called section formula

So, substituting the values in section formula then we can get the co-ordinates of the point P

___________________________________________

So,

${(-1, -7)} = (x_1,y_1)$

${(4,-3)} = (x_2,y_2)$

m : n = 2 : 3

i.e

${x_1 = -1}$

${x_2 = 4}$

${y_1 = -7}$

${y_2 = -3}$

${m= 2}$

${n=3}$

Substituting the values in formula:-

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

$p = \bigg(\dfrac{8 - 3}{5} , \dfrac{ - 6 - 21}{6} \bigg)$

$p = \bigg( \dfrac{5}{5} ,\dfrac{ - 27}{5} \bigg)$

$p = \bigg( 1, \dfrac{ - 27}{5} \bigg)$

So, the co-ordinates of p are (1, -27/5)

Section formulae :-

If a P a point on the line AB we say that P divides the line segment AB internally or externally . If the point P is lie between A and B means it divides internally . If it doesn't lie between them i.e right or left the point it divides externally

Internal division formula :-

If the point A= ${(x_1,y_1)}$ and point B =${(x_2,y_2)}$ divides the point p in ratio m:n internally then the co-ordinates of P are

$p = \bigg( \dfrac{mx_2 + nx_1}{m + n} \dfrac{my_2 + ny_1}{m + n} \bigg)$

External division formula:-

If the point A= ${(x_1,y_1)}$ and point B =${(x_2,y_2)}$ divides the point p in ratio m:n externally then the co-ordinates of P are

$p = \bigg( \dfrac{mx_2 -nx_1}{m - n} \dfrac{my_2 - ny_1}{m - n} \bigg)$

Note :-

Have a look to the attachment which is about the diagram of internal division and external division