Worksheet: Midpoint of a Line Segment

Practice

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

Q1:

Given 𝐴 ( 4 , 8 ) and 𝐵 ( 6 , 6 ) , what are the coordinates of the midpoint of 𝐴 𝐵 ?

  • A ( 7 , 5 )
  • B ( − 1 , 1 )
  • C ( 6 , 6 )
  • D ( 5 , 7 )

Q2:

Given 𝐴 ( 2 , 1 ) and 𝐶 ( − 8 , − 9 ) , what are the coordinates of 𝐵 , if 𝐶 is the midpoint of 𝐴 𝐵 ?

  • A ( 1 0 , 1 0 )
  • B ( − 4 , − 7 )
  • C ( − 3 , − 4 )
  • D ( 1 2 , 1 1 )

Q3:

Consider the points 𝐴 ( 𝑥 , 7 ) , 𝐵 ( − 4 , 𝑦 ) , and 𝐶 ( 2 , 5 ) . Given that 𝐶 is the midpoint of 𝐴 𝐵 , find the values of 𝑥 and 𝑦 .

  • A 𝑥 = − 1 , 𝑦 = 6
  • B 𝑥 = 0 , 𝑦 = 1 7
  • C 𝑥 = 6 , 𝑦 = − 2
  • D 𝑥 = 8 , 𝑦 = 3

Q4:

The origin is the midpoint of the straight segment 𝐴 𝐵 . Find the coordinates of point 𝐵 if the coordinates of point 𝐴 are ( − 6 , 4 ) .

  • A ( − 4 , 6 )
  • B ( − 6 , 4 )
  • C ( − 3 , 2 )
  • D ( 6 , − 4 )

Q5:

Consider the points 𝐴 ( 7 , 7 ) , 𝐵 ( 9 , − 7 ) , and 𝐶 ( 5 , 1 ) . Given that 𝐴 𝐷 is a median of the triangle 𝐴 𝐵 𝐶 and 𝑀 is the midpoint of this median, determine the coordinates of 𝐷 and 𝑀 .

  • A ( 1 , 3 ) , ( − 1 , 2 )
  • B ( 2 , − 4 ) , ( 0 , − 5 )
  • C ( 3 , 1 ) , ( − 5 , 0 )
  • D ( 7 , − 3 ) , ( 7 , 2 )

Q6:

𝐴 , 𝐵 , 𝐶 , and 𝐷 are collinear points. Suppose that the coordinates of points 𝐴 and 𝐶 are ( 2 , 4 ) and ( − 8 , − 8 ) , respectively, and that 𝐴 𝐵 = 𝐵 𝐶 = 𝐶 𝐷 . What are the coordinates of 𝐵 and 𝐷 ?

  • A ( − 1 , 0 ) , ( − 7 , − 8 )
  • B ( 3 , − 8 ) , ( − 1 3 , − 2 4 )
  • C ( 5 , 6 ) , ( − 2 1 , − 2 2 )
  • D ( − 3 , − 2 ) , ( − 1 3 , − 1 4 )

Q7:

If 𝐶 ( − 5 , 4 ) is the midpoint of 𝐴 𝐵 , where 𝐴 ( 𝑥 , 4 ) , 𝐵 ( − 5 , 𝑦 ) , find the values of 𝑥 and 𝑦 .

  • A 𝑥 = − 1 5 , 𝑦 = 1 2
  • B 𝑥 = 4 , 𝑦 = − 5
  • C 𝑥 = − 1 0 , 𝑦 = 8
  • D 𝑥 = − 5 , 𝑦 = 4

Q8:

𝐶 is the midpoint of 𝐴 𝐵 . Find the values of 𝑥 and 𝑦 if the coordinates of 𝐴 , 𝐵 , and 𝐶 are ( 𝑥 , 4 ) , ( 3 , − 2 ) , and ( 9 , 𝑦 ) respectively.

  • A 𝑥 = 1 , 𝑦 = 6
  • B 𝑥 = 2 1 , 𝑦 = 3
  • C 𝑥 = 6 , 𝑦 = 1
  • D 𝑥 = 1 5 , 𝑦 = 1

Q9:

The coordinates of the points 𝐴 , 𝐵 , and 𝐶 in the parallelogram 𝐴 𝐵 𝐶 𝐷 are ( − 2 , − 5 ) , ( − 5 , − 7 ) , and ( − 1 , − 1 3 ) , respectively. If the point 𝐸 lies on 𝐴 𝐷 such that 𝐴 𝐸 = 2 𝐴 𝐷 , determine the coordinates of the points 𝐷 and 𝐸 .

  • A 𝐷 ( − 6 , 1 ) , 𝐸 ( − 1 0 , 7 )
  • B 𝐷 ( 3 , − 1 9 ) , 𝐸 ( 7 , − 2 5 )
  • C 𝐷 ( 2 , − 1 1 ) , 𝐸 ( − 2 , − 5 )
  • D 𝐷 ( 2 , − 1 1 ) , 𝐸 ( 6 , − 1 7 )

Q10:

The point 𝐶 is on ray 𝐴 𝐵 but not segment 𝐴 𝐵 , and its distance from 𝐴 ( 3 , 0 ) is 2 times its distance from 𝐵 ( − 9 , − 6 ) . What are its coordinates?

  • A ( 1 5 , 6 )
  • B ( − 5 , − 4 )
  • C ( − 1 , − 2 )
  • D ( − 2 1 , − 1 2 )

Q11:

Find the values of 𝑎 and 𝑏 so that ( − 2 𝑎 , 2 𝑎 + 𝑏 ) is the midpoint of the line segment between ( − 2 , − 3 ) and ( 2 , 1 1 ) .

  • A 𝑎 = 2 , 𝑏 = − 1 8
  • B 𝑎 = − 2 , 𝑏 = 1 8
  • C 𝑎 = 0 , 𝑏 = 8
  • D 𝑎 = 0 , 𝑏 = 4
  • E 𝑎 = 1 , 𝑏 = − 9

Q12:

Find the point 𝐴 on the 𝑥 -axis and the point 𝐵 on the 𝑦 -axis such that 3 2 , − 5 2 is the midpoint of 𝐴 𝐵 .

  • A ( 3 , 3 ) , ( − 5 , − 5 )
  • B ( 0 , 3 ) , ( − 5 , 0 )
  • C ( 3 , − 5 ) , ( − 5 , 3 )
  • D ( 3 , 0 ) , ( 0 , − 5 )
  • E ( 0 , − 5 ) , ( 3 , 0 )

Q13:

Point ( 2 , − 7 ) is the midpoint of the line segment on endpoints ( 𝑥 , − 9 ) and ( 1 , 𝑦 ) . What is 𝑥 + 𝑦 ?

Q14:

𝐴 ( 3 , 1 7 ) , 𝐹 ( 1 0 , 1 7 ) , 𝐵 ( 1 7 , 1 7 ) , 𝐷 ( 4 , 8 . 5 ) , and 𝐶 ( 1 8 . 5 , 4 . 2 5 ) are points on the trapezoid 𝐴 𝐵 𝐶 𝐷 . If 𝐹 𝐺 is parallel to 𝐴 𝐷 , what is the 𝑥 -coordinate of point 𝐺 ?

Q15:

Suppose the circle of centre 𝑀 − 4 , 1 2 and diameter 𝐴 𝐵 , where 𝐵 ( − 3 , 0 ) . Find the coordinates of 𝐴 , and give the circumference to two decimal places.

  • A 𝐴 ( − 1 1 , 1 ) , 3.93
  • B 𝐴 ( 5 , − 1 ) , 3.51
  • C 𝐴 ( 1 1 , − 1 ) , 7.02
  • D 𝐴 ( − 5 , 1 ) , 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 𝐴 ( 𝑥 , 𝑦 ) and 𝐵 ( 𝑥 , 𝑦 ) .

Find an expression for the midpoint of the line segment 𝐴 𝐵 .

  • A ( 𝑥 + 𝑥 , 𝑦 + 𝑦 )
  • B 𝑥 − 𝑥 2 , 𝑦 − 𝑦 2
  • C ( 𝑥 − 𝑥 , 𝑦 − 𝑦 )
  • D 𝑥 + 𝑥 2 , 𝑦 + 𝑦 2
  • E ( 2 ( 𝑥 + 𝑥 ) , 2 ( 𝑦 + 𝑦 ) )

𝐴 and 𝐵 have the coordinates ( 1 , 1 ) and ( 3 , − 5 ) respectively. Find the midpoint of the line segment 𝐴 𝐵 .

  • A ( 2 , − 2 )
  • B(0, 6)
  • C ( 4 , − 4 )
  • D(0, 3)
  • E ( 8 , − 8 )

Q18:

On the graph, which point is halfway between ( 1 , 8 ) and ( 5 , 2 ) ?

  • A ( 2 , 3 )
  • B ( 5 , 3 )
  • C ( 3 , 2 )
  • D ( 3 , 5 )
  • E ( 4 , 6 )

Q19:

Points 𝐴 and 𝐵 have coordinates ( 3 , 3 ) and ( − 2 , − 5 ) respectively. Is the point 1 2 , − 1 the midpoint of segment 𝐴 𝐵 ?

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

Q20:

Let 𝐴 ( − 3 , − 8 ) , 𝐵 ( − 3 , 6 ) , and 𝐶 ( 3 , − 8 ) be the vertices of a triangle. Suppose that point 𝐷 on 𝐵 𝐶 is such that 𝐴 𝐷 bisects the angle at 𝐴 . What is the point 𝐷 ?

  • A − 6 5 , 9 5
  • B ( 0 , − 1 )
  • C 1 2 7 , − 3 8 7
  • D 6 5 , − 1 9 5

Q21:

Two points 𝐴 and 𝐵 are at ( 1 , 3 ) and ( − 2 , − 5 ) respectively. Point 𝐶 lies on the line segment 𝐴 𝐵 such that the lengths of 𝐴 𝐶 and 𝐶 𝐵 are equal. Find the coordinates of 𝐶 .

  • A 𝐶 = ( − 1 , − 2 )
  • B 𝐶 = 1 2 , 1
  • C 𝐶 = ( 1 , 2 )
  • D 𝐶 = − 1 2 , − 1
  • E 𝐶 = ( − 3 , − 8 )

Q22:

If the coordinates of the points 𝐴 and 𝐵 are ( 2 , 9 ) and ( − 8 , 1 ) respectively, find the midpoint of 𝐴 𝐵 .

  • A ( − 8 , 1 )
  • B ( 2 , 9 )
  • C ( 5 , 5 )
  • D ( − 3 , 5 )

Q23:

Which number is at the midpoint of 𝐴 𝐵 ?

Q24:

If 𝐶 is the midpoint of 𝐴 𝐵 , find the values of 𝑥 and 𝑦 if the coordinates of 𝐴 , 𝐵 , and 𝐶 are ( 9 , − 7 ) , ( 5 , − 5 ) , and ( 𝑥 , 𝑦 ) respectively.

  • A 𝑥 = − 6 , 𝑦 = 7
  • B 𝑥 = 2 , 𝑦 = − 1
  • C 𝑥 = 0 , 𝑦 = 1
  • D 𝑥 = 7 , 𝑦 = − 6

Q25:

Suppose that 𝐴 ( 6 , 1 0 ) and 𝐵 ( 6 , 1 5 ) . What is the midpoint of 𝐴 𝐵 ?

  • A ( 6 , 2 . 5 )
  • B ( 6 , 2 5 )
  • C ( 6 , 5 )
  • D ( 6 , 1 2 . 5 )

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