Solve the problem.
-Show that the point P( , -5, ) is equidistant from the points A( , -7, ) and B( , -3, ).
A) The distance between $\mathrm { P }$ and $\mathrm { A }$ is $\sqrt { 6 }$; the distance between $\mathrm { P }$ and $\mathrm { B }$ is $\sqrt { 6 }$
B) The distance between $\mathrm { P }$ and $\mathrm { A }$ is $\sqrt { 5 }$; the distance between $\mathrm { P }$ and $\mathrm { B }$ is $\sqrt { 5 }$
C) The distance between $\mathrm { P }$ and $\mathrm { A }$ is 2 ; the distance between $\mathrm { P }$ and $\mathrm { B }$ is 2
D) The distance between $\mathrm { P }$ and $\mathrm { A }$ is 3 ; the distance between $\mathrm { P }$ and $\mathrm { B }$ is 3

Question

Solve the problem.
-Show that the point P( , -5, ) is equidistant from the points A( , -7, ) and B( , -3, ). 
A) The distance between $\mathrm { P }$ and $\mathrm { A }$ is $\sqrt { 6 }$; the distance between $\mathrm { P }$ and $\mathrm { B }$ is $\sqrt { 6 }$
B) The distance between $\mathrm { P }$ and $\mathrm { A }$ is $\sqrt { 5 }$; the distance between $\mathrm { P }$ and $\mathrm { B }$ is $\sqrt { 5 }$
C) The distance between $\mathrm { P }$ and $\mathrm { A }$ is 2 ; the distance between $\mathrm { P }$ and $\mathrm { B }$ is 2
D) The distance between $\mathrm { P }$ and $\mathrm { A }$ is 3 ; the distance between $\mathrm { P }$ and $\mathrm { B }$ is 3

Quizplus · Accepted Answer

Let the coordinates of point P be (x, -5, y).
The distance between P and A is:
$$\sqrt{(x-x)^2+(-5+7)^2+(y-0)^2}=\sqrt{4}=2$$
The distance between P and B is:
$$\sqrt{(x-x)^2+(-5+3)^2+(y-0)^2}=\sqrt{4}=2$$
Therefore, P is equidistant from A and B, and the best choice is A.

Solve the Problem P\mathrm { P }P And A\mathrm { A }A

Solve the Problem $\mathrm { P }$ And $\mathrm { A }$