Given:
Line KJ represents a proportional relationship.
Point K lies at (12,14).
To find:
The ordered pair of the coordinates of point J.
Solution:
If y is proportional to x, then
![y\propto x](https://tex.z-dn.net/?f=y%5Cpropto%20x)
![y=kx](https://tex.z-dn.net/?f=y%3Dkx)
![\dfrac{y}{x}=k](https://tex.z-dn.net/?f=%5Cdfrac%7By%7D%7Bx%7D%3Dk)
Where, k is the constant of proportionality.
It means, the ratios of y to x for all the point in a proportional relationship are same.
Line KJ represents a proportional relationship. Point K lies at (12,14).
So, the constant of proportionality is:
![k=\dfrac{14}{12}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7B14%7D%7B12%7D)
![k=\dfrac{7}{6}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7B7%7D%7B6%7D)
Similarly, find the ratio of y to x for all given points.
In option a,
![\dfrac{3.5}{3}=\dfrac{3.5\times 2}{3\times 2}](https://tex.z-dn.net/?f=%5Cdfrac%7B3.5%7D%7B3%7D%3D%5Cdfrac%7B3.5%5Ctimes%202%7D%7B3%5Ctimes%202%7D)
![\dfrac{3.5}{3}=\dfrac{7}{6}](https://tex.z-dn.net/?f=%5Cdfrac%7B3.5%7D%7B3%7D%3D%5Cdfrac%7B7%7D%7B6%7D)
In option b,
![\dfrac{15}{17.5}=\dfrac{15\times 2}{17.5\times 2}](https://tex.z-dn.net/?f=%5Cdfrac%7B15%7D%7B17.5%7D%3D%5Cdfrac%7B15%5Ctimes%202%7D%7B17.5%5Ctimes%202%7D)
![\dfrac{15}{17.5}=\dfrac{30}{35}](https://tex.z-dn.net/?f=%5Cdfrac%7B15%7D%7B17.5%7D%3D%5Cdfrac%7B30%7D%7B35%7D)
![\dfrac{15}{17.5}=\dfrac{6}{7}](https://tex.z-dn.net/?f=%5Cdfrac%7B15%7D%7B17.5%7D%3D%5Cdfrac%7B6%7D%7B7%7D)
In option c,
![\dfrac{0}{2}=0](https://tex.z-dn.net/?f=%5Cdfrac%7B0%7D%7B2%7D%3D0)
In option d,
![\dfrac{3}{3.5}=\dfrac{3\times 2}{3.5\times 2}](https://tex.z-dn.net/?f=%5Cdfrac%7B3%7D%7B3.5%7D%3D%5Cdfrac%7B3%5Ctimes%202%7D%7B3.5%5Ctimes%202%7D)
![\dfrac{3}{3.5}=\dfrac{6}{7}](https://tex.z-dn.net/?f=%5Cdfrac%7B3%7D%7B3.5%7D%3D%5Cdfrac%7B6%7D%7B7%7D)
The ratio of y to x of point (3,3.5) is equal to the ratio of given point K(12,14). So, the coordinates of point J are (3,3.5).
Therefore, the correct option is A.