Question

in the diagram of collinear points, gk = 24, hj = 10, and gh = hi = ij. find each length.

1. hi =
2. jk =
3. ig =
4. ik =

Explanation:

Step1: Find the length of $HI$

Since $HJ = 10$ and $HI=IJ$, then $HI=\frac{HJ}{2}=\frac{10}{2} = 5$.

Step2: Find the length of $JK$

We know $GK = 24$, $GH = HI = 5$. So $GH+HI+IJ+JK=24$. Substituting known values, $5 + 5+5+JK=24$. Then $JK=24-(5 + 5+5)=9$.

Step3: Find the length of $IG$

$IG=IH + HG$. Since $IH = 5$ and $HG = 5$, then $IG=5 + 5=10$.

Step4: Find the length of $IK$

$IK=IJ+JK$. Since $IJ = 5$ and $JK = 9$, then $IK=5 + 9=14$.

Answer:

1. $HI = 5$
2. $JK = 9$
3. $IG = 10$
4. $IK = 14$