Worksheet: Midpoint on the Coordinate Plane

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

Q1:

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

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

Q2:

Given 𝐴(βˆ’8,βˆ’3) and 𝐢(4,1), what are the coordinates of 𝐡 if 𝐢 is the midpoint of 𝐴𝐡?

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

Q3:

Consider the points 𝐴(π‘₯,7),𝐡(βˆ’4,𝑦), and 𝐢(2,5). Given that 𝐢 is the midpoint of 𝐴𝐡, find the values of π‘₯ and 𝑦.

  • A π‘₯ = 8 , 𝑦 = 3
  • B π‘₯ = 0 , 𝑦 = 1 7
  • C π‘₯ = βˆ’ 1 , 𝑦 = 6
  • D π‘₯ = 6 , 𝑦 = βˆ’ 2

Q4:

The origin is the midpoint of the straight segment 𝐴𝐡. Find the coordinates of point 𝐡 if the coordinates of point 𝐴 are (βˆ’6,4).

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

Q5:

Consider the points 𝐴(7,7),𝐡(9,βˆ’7), and 𝐢(5,1). Given that 𝐴𝐷 is a median of the triangle 𝐴𝐡𝐢 and 𝑀 is the midpoint of this median, determine the coordinates of 𝐷 and 𝑀.

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

Q6:

𝐴 , 𝐡 , 𝐢 , and 𝐷 are collinear points. Suppose that the coordinates of points 𝐴 and 𝐢 are (2,4) and (βˆ’8,βˆ’8), respectively, and that 𝐴𝐡=𝐡𝐢=𝐢𝐷. What are the coordinates of 𝐡 and 𝐷?

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

Q7:

If 𝐢(βˆ’5,4) is the midpoint of 𝐴𝐡, where 𝐴(π‘₯,4), 𝐡(βˆ’5,𝑦), find the values of π‘₯ and 𝑦.

  • A π‘₯ = 4 , 𝑦 = βˆ’ 5
  • B π‘₯ = βˆ’ 1 5 , 𝑦 = 1 2
  • C π‘₯ = βˆ’ 1 0 , 𝑦 = 8
  • D π‘₯ = βˆ’ 5 , 𝑦 = 4

Q8:

𝐢 is the midpoint of 𝐴𝐡. Find the values of π‘₯ and 𝑦 if the coordinates of𝐴, 𝐡, and 𝐢 are (π‘₯,4), (3,βˆ’2), and (9,𝑦) respectively.

  • A π‘₯ = 2 1 , 𝑦 = 3
  • B π‘₯ = 6 , 𝑦 = 1
  • C π‘₯ = 1 5 , 𝑦 = 1
  • D π‘₯ = 1 , 𝑦 = 6

Q9:

The coordinates of the points 𝐴, 𝐡, and 𝐢 in the parallelogram 𝐴𝐡𝐢𝐷 are (βˆ’2,βˆ’5), (βˆ’5,βˆ’7), and (βˆ’1,βˆ’13), respectively. If the point 𝐸 lies on 𝐴𝐷 such that 𝐴𝐸=2𝐴𝐷, determine the coordinates of the points 𝐷 and 𝐸.

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

Q10:

The point 𝐢 is on ray 𝐴𝐡 but not segment 𝐴𝐡, and its distance from 𝐴(3,0) is 2 times its distance from 𝐡(βˆ’9,βˆ’6). What are its coordinates?

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

Q11:

Find the values of π‘Ž and 𝑏 so that (βˆ’2π‘Ž,2π‘Ž+𝑏) is the midpoint of the line segment between (βˆ’2,βˆ’3) and (2,11).

  • A π‘Ž = 1 , 𝑏 = βˆ’ 9
  • B π‘Ž = 0 , 𝑏 = 8
  • C π‘Ž = 2 , 𝑏 = βˆ’ 1 8
  • D π‘Ž = 0 , 𝑏 = 4
  • E π‘Ž = βˆ’ 2 , 𝑏 = 1 8

Q12:

Find the point 𝐴 on the π‘₯-axis and the point 𝐡 on the 𝑦-axis such that ο€Ό32,βˆ’52 is the midpoint of 𝐴𝐡.

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

Q13:

Point (2,βˆ’7) is the midpoint of the line segment on endpoints (π‘₯,βˆ’9) and (1,𝑦). What is π‘₯+𝑦?

Q14:

𝐴 ( 3 , 1 7 ) , 𝐹 ( 1 0 , 1 7 ) , 𝐡 ( 1 7 , 1 7 ) , 𝐷 ( 4 , 8 . 5 ) , and 𝐢(18.5,4.25) are points on the trapezoid 𝐴𝐡𝐢𝐷. If 𝐹𝐺 is parallel to 𝐴𝐷, what is the π‘₯-coordinate of point 𝐺?

Q15:

Suppose the circle of center π‘€ο€Όβˆ’4,12 and diameter 𝐴𝐡, where 𝐡(βˆ’3,0). Find the coordinates of 𝐴, and give the circumference to two decimal places.

  • A 𝐴 ( βˆ’ 5 , 1 ) , 7.02
  • B 𝐴 ( βˆ’ 1 1 , 1 ) , 3.93
  • C 𝐴 ( 1 1 , βˆ’ 1 ) , 7.02
  • D 𝐴 ( 5 , βˆ’ 1 ) , 3.51

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

Q17:

Consider the two points 𝐴(π‘₯,𝑦) and 𝐡(π‘₯,𝑦).

Find an expression for the midpoint of the line segment 𝐴𝐡.

  • A ( π‘₯ βˆ’ π‘₯ , 𝑦 βˆ’ 𝑦 )    
  • B ( π‘₯ + π‘₯ , 𝑦 + 𝑦 )    
  • C ο€Ό π‘₯ + π‘₯ 2 , 𝑦 + 𝑦 2     
  • D ( 2 ( π‘₯ + π‘₯ ) , 2 ( 𝑦 + 𝑦 ) )    
  • E ο€» π‘₯ βˆ’ π‘₯ 2 , 𝑦 βˆ’ 𝑦 2     

𝐴 and 𝐡 have the coordinates (1,1) and (3,βˆ’5) respectively. Find the midpoint of the line segment 𝐴𝐡.

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

Q18:

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

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

Q19:

Points 𝐴 and 𝐡 have coordinates (3,3) and (βˆ’2,βˆ’5) respectively. Is the point ο€Ό12,βˆ’1 the midpoint of segment 𝐴𝐡?

  • AWe need more information in order to work it out.
  • Byes
  • Cno

Q20:

Two points 𝐴 and 𝐡 are at (1,3) and (βˆ’2,βˆ’5) respectively. Point 𝐢 lies on the line segment 𝐴𝐡 such that the lengths of 𝐴𝐢 and 𝐢𝐡 are equal. Find the coordinates of 𝐢.

  • A 𝐢 = ( βˆ’ 1 , βˆ’ 2 )
  • B 𝐢 = ( βˆ’ 3 , βˆ’ 8 )
  • C 𝐢 = ο€Ό βˆ’ 1 2 , βˆ’ 1 
  • D 𝐢 = ο€Ό 1 2 , 1 
  • E 𝐢 = ( 1 , 2 )

Q21:

If the coordinates of the points 𝐴 and 𝐡 are (2,9) and (βˆ’8,1) respectively, find the midpoint of 𝐴𝐡.

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

Q22:

Which number is at the midpoint of 𝐴𝐡?

Q23:

If 𝐢 is the midpoint of 𝐴𝐡, find the values of π‘₯ and 𝑦 if the coordinates of 𝐴, 𝐡, and 𝐢 are (9,βˆ’7), (5,βˆ’5), and (π‘₯,𝑦) respectively.

  • A π‘₯ = βˆ’ 6 , 𝑦 = 7
  • B π‘₯ = 0 , 𝑦 = 1
  • C π‘₯ = 2 , 𝑦 = βˆ’ 1
  • D π‘₯ = 7 , 𝑦 = βˆ’ 6

Q24:

Suppose that 𝐴(6,10) and 𝐡(6,15). What is the midpoint of 𝐴𝐡?

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

Q25:

Suppose 𝐴(βˆ’7,βˆ’4), 𝐡(6,βˆ’9), and 𝐷(8,βˆ’2). If 𝐢 is the midpoint of both 𝐴𝐡 and 𝐷𝐸, find 𝐸.

  • A ( 9 , 1 1 )
  • B ( βˆ’ 9 , βˆ’ 1 1 )
  • C ( 2 1 , βˆ’ 7 )
  • D ( βˆ’ 2 1 , 7 )

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