Worksheet: Distance on the Coordinate Plane: Horizontal and Vertical

In this worksheet, we will practice finding the horizontal or vertical distance between two points on the coordinate plane.

Q1:

Find the length of 𝐴𝐡.

Q2:

Find the lengths of 𝐴𝐡 and 𝐷𝐢, where the coordinates of points 𝐴, 𝐡, 𝐢, and 𝐷 are (βˆ’2,3), (5,3), (βˆ’2,βˆ’4), and (βˆ’2,βˆ’5), respectively, considering that a length unit is equal to 1 cm.

  • A 𝐴 𝐡 = 5 c m , 𝐷 𝐢 = 2 c m
  • B 𝐴 𝐡 = 2 c m , 𝐷 𝐢 = 3 c m
  • C 𝐴 𝐡 = 7 c m , 𝐷 𝐢 = 9 c m
  • D 𝐴 𝐡 = 7 c m , 𝐷 𝐢 = 1 c m

Q3:

Given points 𝐢(16,20) and 𝐷(16,10), calculate the distance between the two points, 𝐢 and 𝐷, considering that a length unit =1cm.

Q4:

Use the graph below to determine the points 𝐴, 𝐡, 𝐢, and 𝐷, and find the area of the shape that results from connecting them.

  • A 𝐴 ( βˆ’ 4 , 6 ) , 𝐡 ( βˆ’ 4 , βˆ’ 6 ) , 𝐢 ( 4 , βˆ’ 6 ) , 𝐷 ( 4 , 6 ) , 48
  • B 𝐡 ( βˆ’ 4 , 6 ) , 𝐢 ( βˆ’ 4 , βˆ’ 6 ) , 𝐴 ( 4 , βˆ’ 6 ) , 𝐷 ( 4 , 6 ) , 96
  • C 𝐡 ( βˆ’ 4 , 6 ) , 𝐢 ( βˆ’ 4 , βˆ’ 6 ) , 𝐴 ( 4 , βˆ’ 6 ) , 𝐷 ( 4 , 6 ) , 48
  • D 𝐴 ( βˆ’ 4 , 6 ) , 𝐡 ( βˆ’ 4 , βˆ’ 6 ) , 𝐢 ( 4 , βˆ’ 6 ) , 𝐷 ( 4 , 6 ) , 96

Q5:

Quadrilateral 𝑃𝑄𝑅𝑆 has vertices 𝑃(βˆ’1,6), 𝑄(5,6), 𝑅(5,3), and 𝑆(βˆ’1,3). Find the length of 𝑄𝑆.

  • A 3 √ 5
  • B3
  • C √ 9 7
  • D 5 √ 2
  • E √ 6

Q6:

If 𝐴𝐡𝐢𝐷 is a square, where 𝐴(7,2), 𝐡(π‘₯,𝑦), 𝐢(4,5), and 𝐷(4,2), find the ordered pair (π‘₯,𝑦) that represents 𝐡 and then determine the area of the square considering a unit length =1cm.

  • A 𝐡 ( 7 , 5 ) , area =9cm
  • B 𝐡 ( 5 , 7 ) , area =3cm
  • C 𝐡 ( 7 , 5 ) , area =12cm
  • D 𝐡 ( 5 , 7 ) , area =6cm

Q7:

Use the graph below to determine the coordinates of the points 𝐴, 𝐡, and 𝐢, then find the area of the resulting figure from connecting the points.

  • A 𝐢 ( βˆ’ 2 , 0 ) , 𝐡 ( βˆ’ 2 , 5 ) , 𝐴 ( 2 , 5 ) , 20 area units
  • B 𝐴 ( βˆ’ 2 , 0 ) , 𝐡 ( βˆ’ 2 , 5 ) , 𝐢 ( 2 , 5 ) , 20 area units
  • C 𝐴 ( βˆ’ 2 , 0 ) , 𝐡 ( βˆ’ 2 , 5 ) , 𝐢 ( 2 , 5 ) , 10 area units
  • D 𝐡 ( βˆ’ 2 , 0 ) , 𝐢 ( βˆ’ 2 , 5 ) , 𝐴 ( 2 , 5 ) , 10 area units

Q8:

Given that one length unit equals 1 cm, find the perimeter of 𝐿𝑀𝑁𝐻, where the coordinates of points 𝐿, 𝑀, 𝑁, and 𝐻 are (βˆ’7,βˆ’3), (2,βˆ’3), (2,9), and (βˆ’7,9), respectively.

Q9:

Do the two points (βˆ’5,5) and (βˆ’1,1) lie on the same side of the line 3π‘₯βˆ’2π‘¦βˆ’4=0?

  • Ayes
  • Bno

Q10:

What is the distance between the points (βˆ’8,2) and (βˆ’4,2)?

Q11:

A teacher asked his students to find the distance between the points (5,2) and (βˆ’1,2). Daniel said that the distance is 4, while David said that the distance is 6. Which of them answered correctly?

  • ADaniel
  • BDavid

Q12:

James and Daniel are two friends who go to the same school. James’s room is located at (βˆ’5,6), Daniel’s room at (βˆ’5,βˆ’4), and the band room at (4,βˆ’4).

How far is James’s room from Daniel’s?

What is the distance between Daniel’s room and the band room?

Q13:

In a treasure hunt, a sealed envelope was given to each team. The envelope contained map drawn on a coordinate grid and the following information: the campsite is at the origin point, the campfire at (5,4), the river at (5,βˆ’5), the tent at (βˆ’2,βˆ’5), and the big tree at (βˆ’2,4).

What is the distance between the campfire and the big tree?

What is the distance between the tent and the big tree?

What is the distance between the campfire and the river?

Q14:

Suppose that in the given figure, 𝐡(43.5,βˆ’43.5) and 𝐴 is on the π‘₯-axis. What is the length of 𝐴𝐡?

  • A21.75
  • B43.5
  • C61.52
  • D87

Q15:

Find the length of the base of Triangle B.

Q16:

Anthony graphed the points 𝐴(5,2) and 𝐷(βˆ’1,2). He said that the distance between these points is 4. Do you agree or disagree?

  • Adisagree
  • Bagree

Q17:

Find the distance between point 𝐴, located at (9,βˆ’3), and point 𝐡, located at (4,βˆ’3).

Q18:

What is the distance between the point (5,19) and the 𝑦-axis?

Q19:

Given that the coordinates of the points 𝐴 and 𝐡 are (13,8) and (14,8) respectively, and one unit length =1cm, find the length of 𝐴𝐡.

Q20:

Given that the coordinates of 𝑀 and 𝑁 are (6,5) and (6,11), respectively, determine the length of 𝑀𝑁.

Q21:

Point 𝐻 is located at (βˆ’6,βˆ’2). Which of the following points is 6 units away from point 𝐻?

  • A ( 0 , βˆ’ 6 )
  • B ( βˆ’ 6 , 0 )
  • C ( 4 , βˆ’ 6 )
  • D ( βˆ’ 6 , 4 )
  • E ( βˆ’ 1 2 , 4 )

Q22:

To go to the park from the mall, a straight path is taken which can be represented on a coordinate grid by the points 𝐡=(βˆ’4,1) and 𝐷=(βˆ’4,βˆ’3).

Select the right grid that can be used to represent that path.

  • A
  • B
  • C
  • D
  • E

Find the distance between 𝐡 and 𝐷.

Q23:

In a coordinate plane, James’s middle school lies at (βˆ’4,βˆ’6) and his elementary school at (βˆ’4,3). Each unit in the plane represents 1 mile in reality. If James can ride his bike at a constant rate of 12 miles per hour, how many minutes does it take him to ride from middle school to elementary school?

Q24:

Are the points (0,βˆ’2), (4,βˆ’2), and (8,βˆ’2) collinear?

  • Ayes
  • Bno

Q25:

Given that the coordinates of points 𝐢 and 𝐷 are (7,5) and (7,4) respectively, find the perimeter of the figure 𝐴𝐡𝐢𝐷.

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