Question

Which of the following statements about the distance formula is TRUE?
A. The distance formula cannot be derived from the Pythagorean Theorem. B.The distance formula can be written correctly in several different ways.
C. The distance formula can be written correctly in only one way.
D. The distance formula only applies to points in one dimension.

Answer 1

B is correct.  The distance formula can be written correctly in several different ways.  Examples:

sqrt( change in x)^2 + (change in y)^2 ) 

sqrt( (x2-x1)^2 + (y2-y1)^2 )

Answer 2

The distance formula can be written correctly in several different ways is the true statement.

What is distance?

" Distance is defined as the total length between two points."

According to the question,

Distance can be measured using the following formula for different condition.

• If two coordinates are given as $(x_{1} ,y_{1} )$ and $(x_{2} ,y_{2} )$ , distance between two coordinates can be calculated using distance formula = $\sqrt{(x_{2}- x_{1})^{2}+(y_{2}- y_{1})^{2} }$ derived from Pythagoras theorem.
• Distance can be calculated using speed and time .                     distance = speed ×time
• Distance between point and a line = $\frac{|Ax_{1} +By_{1}+C| }{\sqrt{A^{2}+ B^{2} } }$

Hence, Option(B) is the correct answer.

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