1. **Problem 1: Find the length of KL** Given points I, J, K, L on a line with lengths: - $IJ = 9$ - $JK = 11$ - $IL = 26$ We want to find $KL$. 2. **Formula and rules:** The length of a segment between two points is the sum of the lengths of the smaller segments between those points. Since $IL$ covers $IJ + JK + KL$, we have: $$IL = IJ + JK + KL$$ 3. **Substitute known values:** $$26 = 9 + 11 + KL$$ 4. **Simplify:** $$26 = 20 + KL$$ 5. **Solve for $KL$:** $$KL = 26 - 20$$ $$KL = 6$$ --- 1. **Problem 2: Find the length of HJ** Given points G, H, I, J on a line with lengths: - $GH = 2$ - $HI = 7$ - $IJ = 12$ We want to find $HJ$. 2. **Formula and rules:** The length $HJ$ is the sum of $HI$ and $IJ$ because $H$ to $J$ covers $H$ to $I$ plus $I$ to $J$. So: $$HJ = HI + IJ$$ 3. **Substitute known values:** $$HJ = 7 + 12$$ 4. **Simplify:** $$HJ = 19$$ Since 19 is not an option, let's check the problem carefully. The problem states $GH = 2$, $HI = 7$, $IJ = 12$, and the segment $GJ$ is 21 (2+7+12). But the question asks for $HJ$, which is from $H$ to $J$. $HJ = HI + IJ = 7 + 12 = 19$ No option matches 19, so let's check if the problem meant something else. If $GH = 2$, $HI = 7$, $IJ = 12$, then $GJ = 2 + 7 + 12 = 21$. If the segment $GJ$ is 7 (as per the problem statement "<---------> 7"), then the problem might have a typo or the 7 is the length of $HI$. Assuming $HI = 7$ is correct, then $HJ = HI + IJ = 7 + 12 = 19$. Since 19 is not an option, the closest option is 17, but that is not correct. Therefore, the correct answer based on the data is $HJ = 19$. --- **Final answers:** - $KL = 6$ - $HJ = 19$ (not listed among options)