On a standard number line, point A has coordinate -28 and point B has coordinate 12. Point… — ACT

On a standard number line, point $A$ has coordinate $-28$ and point $B$ has coordinate $12$ . Point $C$ is the midpoint of segment $AB$ . Point $D$ is positioned on the line such that point $B$ is the midpoint of segment $CD$ . What is the distance between point $C$ and point $D$ on the number line?

Cevap: 40

Cevap

The distance between point

C

and point

D

on the number line is 40.

The midpoint

C

of segment

AB

is found by averaging the coordinates:

\frac{-28 + 12}{2} = -8

. Because point

B(12)

is the midpoint of segment

CD

, set up the equation

\frac{-8 + D}{2} = 12

, yielding

D = 32

. The distance between point

C(-8)

and point

D(32)

is the absolute value of their difference:

|32 - (-8)| = 40

Adım Adım Çözüm

Calculate the coordinate of point

C

, which is the midpoint of segment

AB

The coordinate of point

C

-8

The midpoint of two points on a number line is given by their average:

\frac{-28 + 12}{2} = -8

Determine the coordinate of point

D

using the midpoint relationship for segment

CD

The coordinate of point

D

32

Since point

B(12)

is the midpoint of segment

CD

\frac{C + D}{2} = 12 \implies \frac{-8 + D}{2} = 12

, which solves to

D = 32

Find the distance between point

C

and point

D

The distance is

40

Distance on a number line is the absolute value of the difference between coordinates:

|32 - (-8)| = |40| = 40

Anahtar Kavram

Midpoint and Absolute Value Distance on a Number Line

Alternatif Yöntem

Alternatively, note that the distance of segment

AB

|12 - (-28)| = 40

. Since

C

is the midpoint of

AB

, the length of segment

CB

\frac{40}{2} = 20

. Since

B

is the midpoint of segment

CD

, the length of segment

BD

must equal the length of segment

CB

, which is

20

. Therefore, the total distance from

C

D

CB + BD = 20 + 20 = 40

Tahmini Süre:1m 15s

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Alternatif Yöntem

Konular

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