Z (4, 5) and X(7, – 1) are two given points and the point Y divides the line-segment ZX externally in the ratio 4:3. Find the coordinates of Y.

Question

Z (4, 5) and X(7, – 1) are two given points and the point Y divides the line-segment ZX externally in the ratio 4:3. Find the coordinates of Y.

Answer 1

Given that,

Z(4,5)=(x1,y1),

X(7,-1)=(x2,y2)

Point Y divides the segment ZX in the ratio 4:3

hence m=4, n=3

Since it is mentioned in the question that the point Y divides the segment externally we use the section formula for external division,

Formula:

Y={[(mx2-nx1)/(m-n)],[(my2-ny1)/(m-n)]}

Substituting the known values,

={[(4(7)-3(4))/(4-3)],[(4(-1)-3(5)/(4-3)]}

={(28-12)/1,(-4-15)/1} ={16,-19}

The coordinates for the point Y are (16,-19)