Find all values of $y$ such that the distance between $( 2 , y )$ and $( - 10,3 )$ is 13 .
A) $- 2,8$
B) $- 8,2$
C) $- 8 , - 2$
D) 2,8

Question

Quizplus · Accepted Answer

The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in the Cartesian plane is given by the formula $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Plugging in the given points $(2, y)$ and $(-10, 3)$ and setting the distance equal to 13, we get $\sqrt{(-10 - 2)^2 + (3 - y)^2} = 13$. Simplifying, we find $144 + (3 - y)^2 = 169$, which leads to $(3 - y)^2 = 25$. Solving for $y$, we get $y = -2$ and $y = 8$, hence the correct answer is $y = -2, 8$.

Find All Values Of yyy Such That the Distance Between (2,y)( 2 , y )(2,y)

Find All Values Of $y$ Such That the Distance Between $( 2 , y )$