Lesson Worksheet: Midpoint on the Coordinate Plane Mathematics • 11th Grade

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:

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)

Q3:

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

Q4:

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)

Q5:

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)

Q6:

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)

Q7:

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)

Q8:

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

Q9:

Liam plotted the locations of several places in his town in this coordinate plane.

Liam’s house lies halfway between the museum and the movie theater. Find the coordinates at which Liam should graph a point representing his house.

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

Q10:

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

Practice Means Progress

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