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’12,βˆ’5)
  • B(βˆ’2,βˆ’1)
  • C(16,5)
  • D(βˆ’12,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.

  • Aπ‘₯=8, 𝑦=3
  • Bπ‘₯=0, 𝑦=17
  • Cπ‘₯=βˆ’1, 𝑦=6
  • Dπ‘₯=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’21,βˆ’22)
  • B(βˆ’3,βˆ’2), (βˆ’13,βˆ’14)
  • C(3,βˆ’8), (βˆ’13,βˆ’24)
  • 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.

  • Aπ‘₯=4, 𝑦=βˆ’5
  • Bπ‘₯=βˆ’15, 𝑦=12
  • Cπ‘₯=βˆ’10, 𝑦=8
  • Dπ‘₯=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.

  • Aπ‘₯=21, 𝑦=3
  • Bπ‘₯=6, 𝑦=1
  • Cπ‘₯=15, 𝑦=1
  • Dπ‘₯=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.

  • A𝐷(βˆ’6,1), 𝐸(βˆ’10,7)
  • B𝐷(3,βˆ’19), 𝐸(7,βˆ’25)
  • C𝐷(2,βˆ’11), 𝐸(βˆ’2,βˆ’5)
  • D𝐷(2,βˆ’11), 𝐸(6,βˆ’17)

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(15,6)
  • B(βˆ’21,βˆ’12)
  • 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).

  • Aπ‘Ž=1, 𝑏=βˆ’9
  • Bπ‘Ž=0, 𝑏=8
  • Cπ‘Ž=2, 𝑏=βˆ’18
  • Dπ‘Ž=0, 𝑏=4
  • Eπ‘Ž=βˆ’2, 𝑏=18

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(3,17), 𝐹(10,17), 𝐡(17,17), 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.

  • A𝐴(βˆ’5,1), 7.02
  • B𝐴(βˆ’11,1), 3.93
  • C𝐴(11,βˆ’1), 7.02
  • D𝐴(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?

  • A6 m, 6 m
  • B6 m, 3.5 m
  • C3.5 m, 4.5 m
  • D1 m, 3 m
  • E4 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‘₯,π‘¦βˆ’π‘¦)
  • B(π‘₯+π‘₯,𝑦+𝑦)
  • Cο€Όπ‘₯+π‘₯2,𝑦+𝑦2
  • D(2(π‘₯+π‘₯),2(𝑦+𝑦))
  • Eο€»π‘₯βˆ’π‘₯2,π‘¦βˆ’π‘¦2ο‡οŠ§οŠ¨οŠ§οŠ¨

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.

  • A𝐢=(βˆ’1,βˆ’2)
  • B𝐢=(βˆ’3,βˆ’8)
  • C𝐢=ο€Όβˆ’12,βˆ’1
  • D𝐢=ο€Ό12,1
  • E𝐢=(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.

  • Aπ‘₯=βˆ’6, 𝑦=7
  • Bπ‘₯=0, 𝑦=1
  • Cπ‘₯=2, 𝑦=βˆ’1
  • Dπ‘₯=7, 𝑦=βˆ’6

Q24:

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

  • A(6,25)
  • B(6,12.5)
  • 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(9,11)
  • B(βˆ’9,βˆ’11)
  • C(21,βˆ’7)
  • D(βˆ’21,7)

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