Question

check your understanding

1. use the number line to solve each problem.

a. what is kl?
b. what is the coordinate of the midpoint of $overline{kl}$?
c. point c lies between points k and l. the distance between points k and c is $\frac{1}{3}$ of kl. what is the coordinate of point c?
d. point n lies between points c and l. the distance between points c and n is $\frac{3}{4}$ of cl. what is the coordinate of point n?

Explanation:

Step1: Find the coordinates of K and L

The coordinate of K is - 9 and the coordinate of L is 15.

Step2: Calculate the distance KL

Use the formula $d = |x_2 - x_1|$. Here, $x_1=-9$ and $x_2 = 15$. So $KL=|15-(-9)|=|15 + 9|=24$.

Step3: Calculate the mid - point of KL

Use the mid - point formula $M=\frac{x_1 + x_2}{2}$. Substitute $x_1=-9$ and $x_2 = 15$ into the formula: $M=\frac{-9 + 15}{2}=\frac{6}{2}=3$.

Step4: Calculate the coordinate of C

Since the distance between K and C is $\frac{1}{3}$ of KL, and $KL = 24$, the distance between K and C is $\frac{1}{3}\times24 = 8$. Starting from K(-9), moving 8 units to the right, the coordinate of C is $-9+8=-1$.

Step5: Calculate the distance CL

$CL=KL - KC$. Since $KL = 24$ and $KC = 8$, then $CL=24 - 8 = 16$.

Step6: Calculate the coordinate of N

Since the distance between C and N is $\frac{3}{4}$ of CL, and $CL = 16$, the distance between C and N is $\frac{3}{4}\times16 = 12$. Starting from C(-1), moving 12 units to the right, the coordinate of N is $-1+12 = 11$.

Answer:

a. 24
b. 3
c. -1
d. 11