Determine the point P (x, x), which is equidistant from points A (5, -2) and B (6, 5)

Question

Can you help me solve it, please?

Answer 1

Hi Lee,

 

This problem requires you to think of x-y coordinates or the Cartesian Plane.

I also think the point P (x, x) should be replaced by P (x, y).

 

You have two pints A and B with given x and y coordinates. All you need to do is label them on the Cartesian Plane and connect them with a straight line. You are looking for the x and y coordinates of the center of that line, i.e. the midpoint which is equal to P (x, y).

 

Algebraically, this is equivalent to summing the respective coordinates of the points A and B and dividing them by 2.

 

Let's see:

A (5, -2) and  B (6, 5)

difference in x coordinates = 6+5 = 11

difference in y coordinates = 5+ (-2) = 3

 

when we divide them by 2, we get

x = 5.5 and y = 1.5

so these are the coordinates of the center of the line connecting points A and B, i.e. point P.

 

If you do this on a graph paper, you should get the same answer without doing the calculations. This is the beauty of the Cartesian Plane!

Answer 2

The line segment between two points has a Midpoint.  The Midpoint is equidistant from the end points of the line segment.

 

The Midpoint Formula finds the average x-value and the average y-value:

   M ( (x₁+x₂)/2 , (y₁+y₂)/2 )

   M ( (5+6)/2 , (-2+5)/2 )

   M ( 11/2 , 3/2 )

 

The Midpoint is at x=5.5 and y=1.5.