  ### Home > INT2 > Chapter 9 > Lesson 9.2.1 > Problem9-60

9-60.

On graph paper, plot $ΔABC$ with vertices $A(-1, -1),$ $B(1, 9),$ and $C(7, 5)$.

1. What is the midpoint of $\overline{AB}$? Label it point $D$. What is the midpoint of $\overline{BC}$? Label it point $E$.

$D(0, 4)$ and $E(4,7)$

2. What is the length of the midsegment, $\overline{DE}$? Use it to predict the length of $\overline{AC}$.

Use the Pythagorean Theorem.

3. Calculate the length of $\overline{AC}$. Compare it to your prediction from part (b).

$10$ units

4. Determine the coordinates of point $F$ that lies $\frac { 1 } { 4 }$ of the way from point $B$ to point $A$ on $\overline{AB}$ and the coordinates of point $G$ that lies $\frac { 1 } { 4 }$ of the way from point $B$ to point $C$ on $\overline{BC}$. What do you know about $\overline{FG}$ in relation to $\overline{AC}$? Justify your answers.

Point $F$ is $(0.5, 6.5)$ and Point $G$ is $(2.5, 8)$.

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