### Directed Line Segment, Location, Coordinate Plane, Partitions, Point M, Ratio

The key terms of this Maths chapter include Directed Line Segment, Ratio, Fountain, Coordinate Plane, Location, Endpoints, Partitions, Point M, Coordinates, Nearest Tenth, X- and Y- Coordinates of Point, Point P, Number Line, Midpoint – Mathematics Quiz

Explain why partitioning a directed line segment into a ratio of 1:2 is not the same as finding half the length of the directed line segment.

**A ratio of 1:2 means that there are 3 parts in total. One part will be before the desired point, and 2 parts will be after the desired point. This is the same as finding the point that is 1/3 the length. Half the length of the segment would mean there would only be two pieces, each of equal size.**

Fernando and Maria are at opposite sides of a park. They plan to meet later at a fountain that is located somewhere between them. Maria will arrive at the fountain first, before Fernando even leaves his starting location. The ratio of Maria’s starting location to the fountain to Fernando’s starting place is 5:3. What is the location of the fountain? Round to the nearest tenth, if necessary.

**(-1. 0.5)**

In the coordinate plane, the directed line segment from K to N has endpoints at K(-6, -2) and N(8, 3). Point L partitions the directed line segment from K to N in a ratio of 1:2. Point M partitions the directed line segment from L to N in a ratio of 3:1. What are the coordinates of point M? Round to the nearest tenth, if necessary.

**(5.7, 2.2)**

What are the x- and y- coordinates of point E, which partitions the directed line segment from A to B into a ratio of 1:2?

**(0, 1)**

What is the location of point G, which partitions the directed line segment from F to D into an 8:5 ratio?

**1**

If point P is 9/11 of the distance from M to N, then point P partitions the directed line segment from M to N into a ratio.

**9:2**

What are the x- and y- coordinates of point P on the directed line segment from A to B such that P is the length of the line segment from A to B?

**(-4, -5)**

What is the location of point F, which partitions the directed line segment from D to E into a 5:6 ratio?

**1/11**

A student wants to find point C on the directed line segment from A to B on a number line such that the segment is partitioned in a ratio of 3:4. Point A is at -6 and point B is at 2. The student’s work is shown.

Analyze the student’s work. Is the answer correct? Explain.

**No, the student should have added 3 + 4 to get the total number of sections, and used the fraction 3/7 instead of 3/4.**

What are the coordinates of point P on the directed line segment from R to Q such that P is the length of the line segment from R to Q? Round to the nearest tenth, if necessary.

**(-3.5, 2.3)**

Ari is swimming a 25-meter race. After swimming 6 meters, she catches up to Amanda in a ratio of 7:3 from the 6-meter mark. At what meter mark does Ari catch up to Amanda? Round to the nearest tenth, if necessary.

Ari catches up to Amanda at ___ meters.

**19.3**

What are the x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 3:10? Round to the nearest tenth, if necessary.

x = ____

y = ____

**-2.6**

5.2

On a number line, the directed line segment from Q to S has endpoints Q at -8 and S at 12. Point R partitions the directed line segment from Q to S in a 4:1 ratio.

Which expression correctly uses the formula to find the location of point R?

**B: (4/4 + 1)(12 – (-8)) + (-8)**

Genevieve is cutting a 60-inch piece of ribbon into a ratio of 2:3. Since 2 inches are frayed at one end of the ribbon, she will need to start 2 inches in. This is indicated as 2 on the number line.

Where will her cut be located? Round to the nearest tenth.

She will make the cut ____ inches from the end of the ribbon.

**25.2**

The midpoint of a line segment partitions the line segment into a ratio of

**1:1**

What is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1?

**0**

What are the x- and y- coordinates of point P on the directed line segment from K to J such that P is the length of the line segment from K to J?

**(40, 96)**

What are the x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 5:8? Round to the nearest tenth, if necessary.

**(1.2, -4.7)**