Question

name landen mccurdy
worksheet
locating points on a number line
examples 1 and 3
for exercises 1 - 8, refer to the number line.

1. find the coordinate of point n that is $\frac{1}{5}$ of the distance from k to f.
2. find the coordinate of point m such that the ratio of km to mf is 1:2.
3. find the coordinate of point w such that the ratio of kw to wf is 1:1.
4. find the coordinate of point v that is $\frac{2}{3}$ of the distance from k to f.
5. find the coordinate of point g such that the ratio of kg to gf is 4:1.
6. find the coordinate of point a that is $\frac{3}{5}$ of the distance from k to f.
7. find the coordinate of point y that is $\frac{4}{5}$ of the distance from k to f.
8. find the coordinate of point b such that the ratio of kb to bf is 2:3.

Explanation:

Step1: Identify coordinates of K and F

The coordinate of K is 3 and the coordinate of F is 18.

Step2: General formula for finding a point on a number - line

If we want to find a point P that is $\frac{m}{n}$ of the distance from $x_1$ to $x_2$, the formula for the coordinate of P is $x = x_1+\frac{m}{n}(x_2 - x_1)$.

Step3: Solve problem 1

For point N that is $\frac{1}{5}$ of the distance from K to F, using the formula $x=3+\frac{1}{5}(18 - 3)=3 + 3=6$.

Step4: Solve problem 2

The ratio of KM to MF is 1:2, so the point M is $\frac{1}{1 + 2}=\frac{1}{3}$ of the distance from K to F. Then $x=3+\frac{1}{3}(18 - 3)=3 + 5 = 8$.

Step5: Solve problem 3

The ratio of KW to WF is 1:1, so the point W is the mid - point of K and F. Using the mid - point formula $x=\frac{3 + 18}{2}=\frac{21}{2}=10.5$.

Step6: Solve problem 4

For point V that is $\frac{2}{3}$ of the distance from K to F, $x=3+\frac{2}{3}(18 - 3)=3+10 = 13$.

Step7: Solve problem 5

The ratio of KG to GF is 4:1, so the point G is $\frac{4}{4 + 1}=\frac{4}{5}$ of the distance from K to F. Then $x=3+\frac{4}{5}(18 - 3)=3 + 12=15$.

Step8: Solve problem 6

For point A that is $\frac{3}{5}$ of the distance from K to F, $x=3+\frac{3}{5}(18 - 3)=3 + 9=12$.

Step9: Solve problem 7

For point Y that is $\frac{4}{5}$ of the distance from K to F, $x=3+\frac{4}{5}(18 - 3)=3+12 = 15$.

Step10: Solve problem 8

The ratio of KB to BF is 2:3, so the point B is $\frac{2}{2+3}=\frac{2}{5}$ of the distance from K to F. Then $x=3+\frac{2}{5}(18 - 3)=3 + 6=9$.

Answer:

1. 6
2. 8
3. 10.5
4. 13
5. 15
6. 12
7. 15
8. 9