Question

given xz with x(1,9) and z(5,-11) if y lies on xz such that the ratio of xy to xz 1:4, find the coordinates of y

Answer 1

If a segment XZ joining two endpoints X$(x_1,y_1)$ and Z$(x_2,y_2)$ is divided by a point Y(x, y) externally in the ratio of m : n,

Coordinates of the point will be,

x - coordinates → $\frac{mx_2-nx_1}{m-n}$

y - coordinates → $\frac{my_2-ny_1}{m-n}$

If the coordinates of the endpoints X and Z are (1, 9) and (5, -11) respectively and the ratio in which a point Y divides the segment is 1 : 5,

(Since, XY : XZ = 1 : 4 therefore, XY : YZ = 1 : 5)

Therefore, coordinates of Y will be,

x- coordinates → $\frac{1(5)-5(1)}{1-4}=0$

y-coordinates → $\frac{1(-11)-5(9)}{1-5}=\frac{-56}{-4}=14$

Therefore, coordinates of Y will be $(0,14)$.

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