Question

nd the coordinate of the midpoint of each segment.
5.

e the line segment in the ratio given by putting a dot at the partition.
ratio 1:3
ratio 1:3
ratio 2:3
ratio 2:3

Explanation:

Part 1: Find midpoint coordinates

Step1: Midpoint formula

The midpoint coordinate of two points $x_1$ and $x_2$ is $\frac{x_1+x_2}{2}$.

Step2: Calculate midpoint of $E$ and $P$

$E=-3$, $P=-1$
$\frac{-3 + (-1)}{2} = \frac{-4}{2} = -2$

Step3: Calculate midpoint of $S$ and $D$

$S=-1$, $D=3$
$\frac{-1 + 3}{2} = \frac{2}{2} = 1$

Step1: Segment $FB$ (Ratio 1:3)

Total parts = $1+3=4$. The partition is $\frac{1}{4}$ from $F$. On the 4-segment line, mark the 1st point from $F$.

Step2: Segment $FB$ (Ratio 1:3, second line)

Total parts = $1+3=4$. The partition is $\frac{1}{4}$ from $F$. On the 5-point line, mark the point 1 unit from $F$.

Step3: Segment $IJ$ (Ratio 2:3)

Total parts = $2+3=5$. The partition is $\frac{2}{5}$ from $I$. On the 5-segment line, mark the 2nd point from $I$.

Step4: Segment $IJ$ (Ratio 2:3, second line)

Total parts = $2+3=5$. The partition is $\frac{2}{5}$ from $I$. On the 6-point line, mark the point 2 units from $I$.

Answer:

Midpoint of $EP$: $-2$
Midpoint of $SD$: $1$

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Part 2: Partition segments in given ratios