Choice A is correct. It’s given that the ratio of the length of line segment $X Y$ to the length of line segment $Z V$ is $6$ to $1$ , which means $\frac{X Y}{Z V} = \frac{6}{1}$ . It’s given that the length of line segment $X Y$ is $102$ inches. If the length, in inches, of line segment $Z V$ is represented by $l$ , the value of $l$ can be calculated by solving the equation $\frac{102}{l} = \frac{6}{1}$ , or $\frac{102}{l} = 6$ . Multiplying each side of this equation by $l$ yields $102 equals 6 script l$ . Dividing each side of this equation by $6$ yields $17 equals script l$ . Therefore, the length of line segment $Z V$ is $17$ inches.

Choice B is incorrect. This is the length, in inches, of line segment $Z V$ if the length of line segment $X Y$ is $576$ , not $102$ , inches.

Choice C is incorrect. This is the length, in inches, of line segment $X Y$ , not line segment $Z V$ .

Choice D is incorrect. This is the length, in inches, of line segment $Z V$ if the ratio of the length of line segment $X Y$ to the length of line segment $Z V$ is $1$ to $6$ , not $6$ to $1$ .