Question

unit #2 - warmup problem #4: in the diagram below, line segment $overline{hj}$ is drawn with point i on the segment. the length of $overline{hi}$ is represented by $16x - 12$ and the length of $overline{ij}$ is represented by $10x + 30$. if $x = 7$, determine if point i is the midpoint of $overline{hj}$. justify your answer.

Explanation:

Step1: Calculate length of $\overline{HI}$

Substitute $x = 7$ into $16x-12$. So, $16\times7 - 12=112 - 12=100$.

Step2: Calculate length of $\overline{IJ}$

Substitute $x = 7$ into $10x + 30$. So, $10\times7+30=70 + 30=100$.

Step3: Check mid - point condition

Since $\overline{HI}=100$ and $\overline{IJ}=100$, by the definition of a mid - point (a mid - point divides a line segment into two equal parts), point I is the mid - point of $\overline{HJ}$.

Answer:

Point I is the mid - point of $\overline{HJ}$ because $\overline{HI}=\overline{IJ}=100$ when $x = 7$.