Question

the points on a line can be matched one - to - one with the real numbers. the real number that corresponds to a point is the coordinate of the point. the distance between points a and b, written as ab, is the absolute value of the difference of the coordinates of a and b. ab = |x₂ - x₁|. numeric 3 points using the ruler postulate, find the distance between the two points on the number line? numeric 3 points using the ruler postulate, find the distance between the points a and d on the number line?

Explanation:

Step1: Identify coordinates

The coordinate of point A is - 10 and the coordinate of point D is - 1.

Step2: Apply distance formula

According to the Ruler Postulate, the distance \(d\) between two points on a number - line with coordinates \(x_1\) and \(x_2\) is \(d=\vert x_2 - x_1\vert\). Let \(x_1=-10\) and \(x_2 = - 1\). Then \(d=\vert-1-(-10)\vert\).

Step3: Simplify the expression

\(\vert-1-(-10)\vert=\vert-1 + 10\vert=\vert9\vert = 9\).

Answer:

9