# Worksheet: Partitioning a Line Segment on the Coordinate Plane

In this worksheet, we will practice finding the coordinates of a point that divides a line segment on the coordinate plane with a ratio using the section formula.

**Q2: **

The coordinates of points and are and respectively. Given that intersects the -axis at and the -axis at , find the ratio by which is divided by points and respectively showing the type of division in each case.

- Ainternal division by ratio , external division by ratio
- Binternal division by ratio , external division by ratio
- Cinternal division by ratio , external division by ratio
- Dinternal division by ratio , external division by ratio

**Q3: **

The coordinates of and are and respectively. Determine the coordinates of the points that divide into four equal parts.

- A , ,
- B , ,
- C , ,
- D , ,

**Q4: **

A bus is travelling from city to city . Its first stop is at , which is halfway between the cities. Its second stop is at , which is two-thirds of the way from to . What are the coordinates of and ?

- A ,
- B ,
- C ,
- D ,

**Q5: **

Given and , what are the points and that divide into three parts of equal length?

- A ,
- B ,
- C ,
- D ,

**Q7: **

Consider points and . Find the coordinates of , given that is on the ray but NOT on the segment and .

- A
- B
- C
- D

**Q8: **

Given and , find the coordinates of on for which .

- A ,
- B ,
- C ,
- D ,

**Q9: **

The coordinates of the points and are and respectively. Determine the coordinates of the point , given that it divides externally in the ratio .

- A
- B
- C
- D

**Q10: **

Suppose and another point , and that divides internally in the ratio . What are the coordinates of ?

- A
- B
- C
- D

**Q11: **

Line segment is a median in , where and . Find the point of intersection of the medians of the triangle .

- A
- B
- C
- D

**Q12: **

Find the ratio by which the -axis divides the line segment , joining points and , showing the type of division, and determine the coordinates of the point of division.

- A internally,
- B internally,
- C externally ,
- D externally,

**Q13: **

Given that the coordinates of the points and are and respectively, determine, in vector form, the coordinates of the point , which divides internally in the ratio .

- A
- B
- C
- D

**Q14: **

Given points and , find the ratio by which the divided line segment , together with the type of division. Determine the coordinates of the point of intersection.

- A externally,
- B externally,
- C internally,
- D internally,

**Q15: **

If the coordinates of the points and are and , respectively, find the ratio by which the point divides stating whether it is divided internally or externally, then determine the value of .

- A externally ,
- B externally ,
- C internally,
- D internally,

**Q16: **

If and , find in vector form the coordinates of point which divides externally in the ratio .

- A
- B
- C
- D

**Q17: **

If , , , , is the midpoint of , and divides externally by the ratio , find the length of to the nearest hundredth considering a length unit .

**Q19: **

The coordinates of the points and are and respectively. Determine the coordinates of the point , given that it divides externally in the ratio .

- A
- B
- C
- D

**Q20: **

The coordinates of points and are and respectively. Given that intersects the -axis at and the -axis at , find the ratio by which is divided by points and respectively showing the type of division in each case.

- Ainternal division by ratio , external division by ratio
- Binternal division by ratio , external division by ratio
- Cinternal division by ratio , external division by ratio
- Dinternal division by ratio , external division by ratio

**Q21: **

Two points and are at and respectively. Point lies on the line segment such that the length of is of . Find the coordinates of .

- A
- B
- C
- D
- E

**Q22: **

Two points and are at and respectively. Point lies on the line segment such that the length of is of . Find the coordinates of .

- A
- B
- C
- D
- E

**Q23: **

Two points and are at and respectively. Point lies on the line segment such that the lengths of and are in the ratio of . Find the coordinates of .

- A
- B
- C
- D
- E

**Q24: **

Two points and are at and respectively. Point lies on the line segment such that the lengths of and are in the ratio of . Find the coordinates of .

- A
- B
- C
- D
- E

**Q25: **

A quadrilateral has its vertices at the points , , , and . A point lies on such that the lengths of and are in the ratio of , and a point lies on such that the lengths of and are in the ratio of .

Find the coordinates of .

- A
- B
- C
- D
- E

Find the coordinates of .

- A
- B
- C
- D
- E

Find the slope of the line .

Find the equation of the line , giving your answer in the form .

- A
- B
- C
- D
- E