Question

the diagram of collinear points is shown below. if gi = hj and gh = 3 and gi = 14 then what is the length of ij?

Explanation:

Step1: Identify segment - length relationships

Since \(GI = HJ\) and \(GI=14\), then \(HJ = 14\). Also, \(GH = 3\).

Step2: Use segment - addition postulate

We know that \(GJ=GH + HI+IJ\), and \(GI = GH+HI = 14\), \(HJ=HI + IJ=14\). We want to find \(IJ\).
We know that \(GI=14\) and \(GH = 3\), so \(HI=GI - GH\).
\(HI=14 - 3=11\).
Since \(HJ = HI+IJ\) and \(HJ = 14\), \(HI = 11\), then \(IJ=HJ - HI\).
\(IJ=14 - 11 = 11\).

Answer:

11