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

Answer:-

Given :

Z = (4 , 5)

X = (7 , - 1)

Y divides the line - Segment in the ratio 4 : 3 externally.

Let m = 4 and n = 3

We know that,

The point which divide a line - Segment joining the points (a , b) and (p , q) in the ratio m : n externally is,

$(x \: , \: y) = [ \frac{(m \times p) - (n \times a )}{m - n} \: , \: \frac{(m \times q) - ( n \times b)}{m - n} ] \\ \\ (x \: , \: y) = [\frac{(4 \times 7) - (3 \times 4)}{4 - 3} \:, \: \frac{(4 \times ( - 1)) - (3 \times 5)}{4 - 3}] \\ \\ (x \:, \: y) = [\frac{28 - 12}{1} \: , \: \frac{ - 4 - 15}{ 1} ] \\ \\ (x \: ,\: y) = (16 \: , \: - 19)$

Y(x , y) = (16 , - 19)

Hence, the Coordinates of Y are (x , y) = (16 , - 19).