# Worksheet: Midpoint of a Line Segment

In this worksheet, we will practice finding the coordinates of the midpoint between two points or those of an endpoint on the coordinate plane.

**Q3: **

Consider the points , and . Given that is the midpoint of , find the values of and .

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

**Q4: **

The origin is the midpoint of the straight segment . Find the coordinates of point if the coordinates of point are .

- A
- B
- C
- D

**Q5: **

Consider the points , and . Given that is a median of the triangle and is the midpoint of this median, determine the coordinates of and .

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

**Q6: **

, , , and are collinear points. Suppose that the coordinates of points and are and , respectively, and that . What are the coordinates of and ?

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

**Q7: **

If is the midpoint of , where , , find the values of and .

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

**Q8: **

is the midpoint of . Find the values of and if the coordinates of, , and are , , and respectively.

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

**Q9: **

The coordinates of the points , , and in the parallelogram are , , and , respectively. If the point lies on such that , determine the coordinates of the points and .

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

**Q10: **

The point is on ray but not segment , and its distance from is 2 times its distance from . What are its coordinates?

- A
- B
- C
- D

**Q11: **

Find the values of and so that is the midpoint of the line segment between and .

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

**Q14: **

, , , , and are points on the trapezoid . If is parallel to , what is the -coordinate of point ?

**Q15: **

Suppose the circle of centre and diameter , where . Find the coordinates of , and give the circumference to two decimal places.

- A , 3.93
- B , 3.51
- C , 7.02
- D , 7.02

**Q16: **

A rectangular garden is next to a house along a road. In the garden is an orange tree 7 m from the house and 3 m from the road. There is also an apple tree, 5 m from the house and 9 m from the road. A fountain is placed halfway between the trees. How far is the fountain from the house and the road?

- A 1 m, 3 m
- B 3.5 m, 4.5 m
- C 6 m, 3.5 m
- D 6 m, 6 m
- E 4 m, 8 m

**Q17: **

Consider the two points and .

Find an expression for the midpoint of the line segment .

- A
- B
- C
- D
- E

and have the coordinates and respectively. Find the midpoint of the line segment .

- A
- B(0, 6)
- C
- D(0, 3)
- E

**Q18: **

On the graph, which point is halfway between and ?

- A
- B
- C
- D
- E

**Q19: **

Points and have coordinates and respectively. Is the point the midpoint of segment ?

- A We need more information in order to work it out.
- B no
- C yes

**Q20: **

Let , , and be the vertices of a triangle. Suppose that point on is such that bisects the angle at . What is the point ?

- A
- B
- C
- D

**Q21: **

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

- A
- B
- C
- D
- E

**Q22: **

If the coordinates of the points and are and respectively, find the midpoint of .

- A
- B
- C
- D

**Q23: **

Which number is at the midpoint of ?

**Q24: **

If is the midpoint of , find the values of and if the coordinates of , , and are , , and respectively.

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

**Q25: **

Suppose that and . What is the midpoint of ?

- A
- B
- C
- D