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explain why the dinstance formula is not needed to find the distance between two points that lie on a horinzontal or vertical line

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AL2006
The distance formula is

             D = square root of [ (difference in 'y')² + (difference in 'x')² ]

If the two points are on the same vertical line, the difference in 'x' is zero.
If they're on the same horizontal line, then their difference in 'y' is zero.

Either way, one of the terms in the distance formula is zero.  It goes away,
and the distance formula becomes ...

               D = square root of [ (difference in one coordinate)² ] .

That's just the square root of something squared, so it's only

               D  =  (difference in one coordinate)   

without going through all the squaring and rooting business.
xero099

The Length Equation of the Line Segment is not necessary for horizontal Lines as [tex]\Delta y = 0[/tex] and [tex]\Delta r = \Delta x[/tex] and for vertical Lines as [tex]\Delta x = 0[/tex] and [tex]\Delta r = \Delta y[/tex].

The Length Equation of the Line Segment is an application of the Pythagorean Theorem, which is defined by the following expression:

[tex]\Delta r = \sqrt{(\Delta x)^{2}+(\Delta y)^{2}}[/tex] (1)

Where:

[tex]\Delta x[/tex] - Change in horizontal direction.

[tex]\Delta y[/tex] - Change in vertical direction.

[tex]\Delta r[/tex] - Change along the line segment.

If the Line is horizontal, then [tex]\Delta y = 0[/tex] and [tex]\Delta r = \Delta x[/tex], but if the Line is vertical, then [tex]\Delta x = 0[/tex] and [tex]\Delta r = \Delta y[/tex], meaning that it is not necessary to use in these two cases.

Please see this related question for further details: https://brainly.com/question/17248544

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