Find the value of the unknown coordinate so that the distance between the points is as given.
-$( 1,4 )$ and $( 6 , y )$; distance is 13
A) $y = 148 , y = - 190$
B) $y = 12 , y = - 4$
C) $y = 16 , y = - 8$
D) $y = 17.93 , y = - 9.93$

Question

Quizplus · Accepted Answer

Using the distance formula $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} = 13$, solve for $y$: $\sqrt{(6-1)^2 + (y-4)^2} = 13$. Simplifying gives $(y-4)^2 = 144$, so $y-4 = 12$ or $y-4 = -12$, leading to $y = 16$ or $y = -8$.

Find the Value of the Unknown Coordinate So That the Distance