Question

on a number line, the coordinates of x, y, z, and w are -8, -6, 2, and 5, respectively. find the lengths of the two segments below. then tell whether they are congruent. (overline{zx}) and (overline{wy}) the length of (overline{zx}) is (square) (type an integer or a decimal.)

Explanation:

Step1: Recall the formula for the length of a segment on a number line.

The length of a segment with endpoints having coordinates \(a\) and \(b\) is given by \(|a - b|\) (or \(|b - a|\), since absolute value is commutative).

Step2: Identify the coordinates of \(Z\) and \(X\).

From the problem, the coordinate of \(Z\) is \(2\) and the coordinate of \(X\) is \(-8\).

Step3: Calculate the length of \(\overline{ZX}\).

Using the formula for the length of a segment on a number line, we substitute \(a = 2\) and \(b=-8\) into \(|a - b|\). So we have \(|2-(-8)|\). Simplifying the expression inside the absolute value: \(2 - (-8)=2 + 8 = 10\). Then, \(|10| = 10\).

Answer:

10