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The distance between two points, a and b, on a number line is expressed as
|a – b|, where a and b are rational numbers. Think about locating a point halfway between a and b on a number line. How can you find the coordinate for such a point? Develop a formula in terms of a and b that you can use to find the coordinate. Your formula must work for positive and negative values of a and b. Does absolute value play a role in your formula? Why or why not? Under what circumstances might your formula be used in the real world? Explain.

Discuss how you can find the coordinate of a point located other fractional distances from a to b (or from b to a). For example, locate a point three-fourths of the distance from a to b. What kind of calculation is involved?

Respuesta :

MrRoyal

The distance between points (a) and (b) is the number of units between the points.

Formula for halfway two

Assume the lesser point is point (a)

To locate the halfway between points (a) and (b)

  • Calculate the absolute difference between points (a) and (b) i.e. |a - b|
  • Divide the difference into halves
  • Add the value of one half to point (a).

The above steps is represented as:

[tex]P = a + \frac{|a - b|}{2}[/tex]

Using the above formula, the halfway point between 5 and 11 would be 8

The formula can be used to calculate the distance between negative points, and absolute values are used to determine the number of units between the points

Real world circumstance

The formula can be used to calculate the halfway distance between two points on a track

Fractional distance

To determine the fractional distance, we simply replace the 1/2 in the original formula with the appropriate fraction.

Take for instance, three-fourths from (a) to (b) would be:

[tex]P = a + \frac{3|a - b|}{4}[/tex]

Read more about distance at:

https://brainly.com/question/9935574

angelisagobin

Answer:

The distance between two points is the number of units between them.

Halfway points (a) and (b)

To locate a point halfway points (a) and (b), we use the following steps

Calculate the absolute difference between both points

Divide the absolute difference by 2

Add the quotient to the smaller point.

 

Assume the smaller value is (a), the point (P) halfway points (a) and (b) would be

Take for instance, a = 5, and b = 10.

The halfway point would be:

The halfway point between 5 and 10 is 7.5

The formula works for negative values, and absolute values are used to return the actual difference between both points

Real world circumstance

The formula can be used to calculate the halfway distance between a school gate and the school library (as an instance)

Fractional distance

To determine the fractional distance, we simply replace the 1/2 in the original formula with the appropriate fraction.

Take for instance, three-fourths from (a) to (b) would be:

p = a  +  3|a-b|/4

Step-by-step explanation:

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