Find the value of the unknown coordinate so that the distance between the points is as given.
-$( 3,6.25 )$ and $( x , - 1.75 )$; distance is 10
A) $x = - 3 , x = 9$
B) $x = - 2 , x = 10$
C) $x = 0 , x = 12$
D) $x = 1 , x = 13$

Question

Quizplus · Accepted Answer

The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Substituting the given values, we get $\sqrt{(x - 3)^2 + (-1.75 - 6.25)^2} = 10$. Simplifying inside the square root gives $\sqrt{(x - 3)^2 + (-8)^2} = 10$, which further simplifies to $\sqrt{(x - 3)^2 + 64} = 10$. Squaring both sides gives $(x - 3)^2 + 64 = 100$, leading to $(x - 3)^2 = 36$. Solving for $x$ gives $x - 3 = \pm6$, which results in $x = -3$ or $x = 9$.

Find the Value of the Unknown Coordinate So That the Distance