Question

find the coordinates of p so that p partitions segment ab in the part to whole ratio of 1 to 4 with a(-5,4) and b(7,-4)

Answer 1

`p(x,y) = (-2.6 ,2.4)`

Explanation:

Given

a(-5,4) and b(7,-4)

Required

Partition P

Given that the segment ab is divided into ratio;

The coordinates of point p can be calculated using ratio formula given below

`p(x,y) = ((mx_2 + nx_1)/(m+n) ,(my_2 + ny_1)/(m+n))`

Where m and n are the ratio; m = 1 and n = 4

`(x_1, y_1) = (-5,4); \\(x_2, y_2) = (7,-4)`

So,

`p(x,y) = ((mx_2 + nx_1)/(m+n) ,(my_2 + ny_1)/(m+n))` becomes

`p(x,y) = ((1 *7 + 4 * -5)/(1+4) ,(1 * -4 + 4 * 4)/(1+4))`

`p(x,y) = ((7 + -20)/(5) ,(-4 + 16)/(5))`

`p(x,y) = ((-13)/(5) ,(12)/(5))`

`p(x,y) = (-2.6 ,2.4)`

Hence, the coordinates of p are (-2.6,2.4)