find the distance between (-5,4) and (5,4)?

Method 1 :

The y-coordinate of the two points are equal.
Thus, the line segment joining the two points is horizontal.

Distance between the two points
= Distance between -5 and 5
= 5 - (-5)
= 10


Method 2 :

Distance between two points (x₁, y₁) and (x₂, y₂)
= √[(x₁ - x₂)² + (y₁ - y₂)²]

Distance between (-5, 4) and (5, 4)
= √[(-5 - 5)² + (4 - 4)²]
= √(-10)²
= √100
= 10

5 - -5 = 10

Since this line is parallel to the x-axis ( the value of y does not change), then you simply subtract the x-values, then use the absolute value of the result.

And don't forget that when you subtract, it changes the sign.

If you do -5 - 5 = -10
the distance is |-10| = 10 (distances are never negative)

If you do 5 - (-5) = 5 + 5 = 10
you get the same distance.

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You can still use the comple Pythagorean formula:

d^2 = (diff. in x)^2 + (diff. in y)^2
and you will get
d^2 = (10)^2 + (0)^2
d^2 = (10)^2
square root
d = 10 (not "plus-or-minus" as negative distances don't exist)

Even if you use -10 as the difference in x

d^2 = (-10)^2 + 0^2
d^2 = 100
d = 10