Segments, Length, and Distance: Practice

Segment addition gives $(3x-2)+(x+10)=6x$. Thus $4x+8=6x$, so $x=4$.

$BC=4+10=14$

The other part is $10$ and the whole is $24$, so the positive lengths check: $10+14=24$.

The midpoint gives $AM=40/2=20$. Point $B$ splits that half into $AB$ and $BM$.

$BM=20-13=7$

The distance from $J$ to the midpoint is $5-(-14)=19$. The whole segment has two equal halves.

$JK=2(19)=38$

The other endpoint can be $-10$ or $6$. Half the segment length is $4$, so the midpoint is four units to either side of $P$.

$-2-4=-6$

$-2+4=2$

The whole length is twice a midpoint half: $2x+12=2(3x-4)$. Expanding gives $2x+12=6x-8$, so $x=5$.

$AB=2(5)+12=22$

The half length is $3(5)-4=11$, as required.

The crossing coordinate equals the average of the endpoints.

$\frac{-11+19}{2}=4$

It is therefore the midpoint. Passing through it establishes bisection, while the crossing angle remains unspecified.

Convert $35$ millimeters to $3.5$ centimeters. Then add all three adjacent lengths.

$RU=4.2+3.5+1.3=9\text{ cm}$

Let $BC=t$. Then $AB=2t$, and segment addition gives $2t+t=45$, so $t=15$.

$AB=2(15)=30$

The midpoint reading is the average of the endpoint readings.

$\frac{23+79}{2}=51\text{ mm}$

This coordinate is $5.1$ centimeters.

Half the length is $28$ millimeters, but that is not the midpoint's reading because the segment starts at $23$ millimeters.

The first midpoint makes $AB=BC$. The second makes $BC=CD$. All three adjacent parts therefore have length $6.5$.

$AD=6.5+6.5+6.5=19.5$

The square-corner mark gives perpendicularity. No given information says the crossing point is the midpoint, so equal halves and bisection do not follow.

Each endpoint is half the length, or $7$ units, from the midpoint.

$-3-7=-10$

$-3+7=4$

Their distance is $14$ and their average is $-3$.