Question

What would be the point that partitions segment AB into a 2:1 ratio

Answer 1

Given:

The coordinates of line segment AB are given as follows:

`\begin{gathered} A\text{ \lparen x}_1,y_1)\text{ = \lparen1,3 \rparen} \\ B(x_2,y_2)\text{ = \lparen 7,8 \rparen} \\ m\text{ : n = 2 : 1} \end{gathered}`

Required:

Coordinate of point which divides the given line segment in a ratio of 2:1.

Assume the required point as P(x,y).

Step-by-step explanation:

The required coordinate of point P is calculated using the section formula for internal division.

`P(x,y)\text{ = }(mx_2+nx_1)/(m+n)\text{ , }(my_2+ny_1)/(m+n)`

Substituting the values in the formula,

`\begin{gathered} P(x,y)\text{ = \lbrack }\frac{2(7)\text{ + 1\lparen1\rparen}}{2+1}\text{ , }(2(8)+1(3))/(2+1)\text{ \rbrack} \\ P(x,y)\text{ = \lbrack }\frac{14\text{ + 1}}{3}\text{ , }\frac{16\text{ + 3}}{3}\text{ \rbrack} \\ P(x,y)\text{ = \lbrack }(15)/(3)\text{ , }(19)/(3)\text{ \rbrack} \\ P(x,y)\text{ = \lbrack 5 , }(19)/(3)\text{ \rbrack} \\ \end{gathered}`

Answer:

Thus the coordinate of the point P(x,y) which divides the line segment Ab in a ration 2 : 1 is,