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Find the distance between each pair of points and the midpoint of (5,6) and (5,0).
To get the distance between the two given points, let us use the formula:
[tex] \sf D= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} [/tex]
wherein,
[tex]\sf D= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\sf D= \sqrt{(5-5)^2+(0-6)^2}[/tex]
[tex]\sf D= \sqrt{(0)^2+(-6)^2}[/tex]
[tex]\sf D= \sqrt{0+36}[/tex]
[tex]\sf D= \sqrt{36}[/tex]
[tex]\boxed{\sf D= 6}[/tex]
The distance between the two given points is 6 units.
Another thing, without using the formula, we can easily tell the distance between two points if they lie on the same line parallel to x or y axis. All you need to do is to add the absolute values of the numbers that are different, x coordinates or y coordinates.
To get the midpoint of the two given points that lies on the same line parallel to x or y axis (the x coordinate is constant in the problem), let's just divide the distance by two (for y coordinate).
Also, you can use the formula in finding the midpoint of two distinct points.
[tex]\sf M=(\frac{x_1+x_2}{2}, {y_1+y_2}{2})[/tex]
[tex]\sf M=(\frac{5+5}{2}, {6+0}{2})[/tex]
[tex]\sf M=(\frac{10}{2}, {6}{2})[/tex]
[tex]\boxed{\sf M=(5, 3)}[/tex]
The midpoint is (5, 3).