Question

look at the diagram and evaluate. which of the statements below is false? answer vw = wx ux > uw w is the midpoint of vx vw > uv

Explanation:

Step1: Determine the lengths of line - segments

From the number - line, the coordinate of \(U = 3\), \(V = 13\), \(W = 16\), \(X = 19\).
The length of a line - segment with endpoints \(a\) and \(b\) is given by \(|a - b|\).
\(VW=|16 - 13| = 3\), \(WX=|19 - 16| = 3\), \(UX=|19 - 3| = 16\), \(UW=|16 - 3| = 13\), \(UV=|13 - 3| = 10\).

Step2: Check each statement

• For \(VW = WX\): Since \(VW = 3\) and \(WX = 3\), \(VW = WX\) is True.
• For \(UX>UW\): Since \(UX = 16\) and \(UW = 13\), \(UX>UW\) is True.
• For \(W\) is the mid - point of \(\overline{VX}\): The mid - point of two points \(x_1\) and \(x_2\) is \(\frac{x_1 + x_2}{2}\). The mid - point of \(V(13)\) and \(X(19)\) is \(\frac{13+19}{2}=\frac{32}{2}=16\), which is the coordinate of \(W\), so \(W\) is the mid - point of \(\overline{VX}\) is True.
• For \(VW>UV\): Since \(VW = 3\) and \(UV = 10\), \(VW>UV\) is False.

Answer:

VW > UV