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
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
[tex]\dfrac{y}{x}=k[/tex]
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:
[tex]k=\dfrac{14}{12}[/tex]
[tex]k=\dfrac{7}{6}[/tex]
Similarly, find the ratio of y to x for all given points.
In option a,
[tex]\dfrac{3.5}{3}=\dfrac{3.5\times 2}{3\times 2}[/tex]
[tex]\dfrac{3.5}{3}=\dfrac{7}{6}[/tex]
In option b,
[tex]\dfrac{15}{17.5}=\dfrac{15\times 2}{17.5\times 2}[/tex]
[tex]\dfrac{15}{17.5}=\dfrac{30}{35}[/tex]
[tex]\dfrac{15}{17.5}=\dfrac{6}{7}[/tex]
In option c,
[tex]\dfrac{0}{2}=0[/tex]
In option d,
[tex]\dfrac{3}{3.5}=\dfrac{3\times 2}{3.5\times 2}[/tex]
[tex]\dfrac{3}{3.5}=\dfrac{6}{7}[/tex]
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.
