Solved Examples and Worksheet for Counting Distance on a Horizontal or Vertical Line

Q1What is the distance between the letters Q and R?


A. 4 units
B. 2 units
C. 3 units
D. 1 unit

Solutions
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Step: 1
The line joining the letters Q and R is a horizontal line segment.
Step: 2
The length of a horizontal line segment on a coordinate plane equals the difference between the x-coordinates.
Step: 3
The letter Q is located on the ordered pair (4, 4) and the letter R is located on the ordered pair (5, 4).
Step: 4
So, the distance between the letter Q and R = 5 - 4 = 1
  [Difference between the x-coordinates.]
Step: 5
The distance between the letters Q and R is 1 unit.
Correct Answer is :   1 unit
Q2Sony is at point C and his friend is at point A. He wants to meet his friend. Which of the following represents his path from C to A?


A. move 4 units east and 3 units south
B. move 4 units west and 3 units south
C. move 3 units east and 4 units north
D. move 3 units west and 4 units north

Solutions
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Step: 1
Locate points C and A on the grid. Using (x,y) coordinates, point C is at (5,4) and point A is at (1,1).
Step: 2
To find the horizontal distance, subtract the x-coordinates: 5-1=4 units in the westward direction moving from C to A.
Step: 3
To find the vertical distance, subtract the y-coordinates: 4-1=3 units in the southward direction moving from C to A.
Step: 4
Therefore Sony must move 4 units west and 3 units south to meet up with this friend.
Correct Answer is :   move 4 units west and 3 units south
Q3The path taken by George to reach his school from house is 3 units up and 4 units right. Find the shortest distance between the house and school.
A. 7 units
B. 3 units
C. 4 units
D. 5 units

Solutions
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Step: 1
Mark the distance traveled on the coordinate plane.
Step: 2
The end points are (1, 1) and (4, 5).
Step: 3
The shortest distance between the house and the school is the distance between the end points
Step: 4
The distance between two points A(x1, y1) and B(x2, y2) is (x2-x1)²+(y2-y1)²
Step: 5
The distance is (4-1)²+(5-1)² = 25 = 5 units
Step: 6
Hence the shortest distance between the house and the school is 5 units.
Correct Answer is :   5 units
Q4Find the distance between the Library and the Complex.


A. 5 units
B. 3 units
C. 4 units
D. 6 units

Solutions
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Step: 1
By observing the chart, from the library if we move 4 units to south we will be at the complex.
Step: 2
So, the distance between Library and Complex is 4 units.
Correct Answer is :   4 units
Q5Suzan went to Play Zone Park on last Sunday. At first she played at the pool, and after sometime, she moved to slides. Which of the following represents the possible path from pool to slides?

A. move 3 units east and 2 units north
B. move 2 units north and 3 units east
C. move 2 units south and 2 units east
D. move 3 units north and 2 units east

Solutions
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Step: 1
The possible path from pool to slides is moving 3 units north and 2 units east.
Correct Answer is :   move 3 units north and 2 units east
Q6Which of the following describes the path from the bee to the chicken?


A. 4 units left and 3 units up
B. 3 units up and 3 units left
C. 3 units up and 4 units right
D. 3 units down and 3 units left

Solutions
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Step: 1
The chicken is located 4 units left and 3 units up from the location of the bee as shown in the figure below.
Correct Answer is :   4 units left and 3 units up
Q7Joseph stays at flower. How can he reach chicken?


A. 2 units up and 1 unit right
B. 1 unit down and 3 units left
C. 3 units down and 2 units left
D. 3 units up and 1 unit left

Solutions
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Step: 1
The chicken is located 3 units down and 2 units left from the location of the flower as shown in the figure.
Correct Answer is :   3 units down and 2 units left
Q8How can fish reach bee on the grid shown?


A. 2 units down and 2 units right
B. 2 units down and 1 unit right
C. 1 unit down and 2 units right
D. 2 units up and 2 units right

Solutions
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Step: 1
The bee is located 2 units down and 2 units right from the location of the fish as shown in the figure below.
Correct Answer is :   2 units down and 2 units right
Q9Compute the distance between the points A and D.

A. 4 units
B. 6 units
C. 2 units
D. 0 units

Solutions
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Step: 1
The distance between A and D = 2 - (- 2)
  [Difference between the y-coordinates.]
Step: 2
= 4 units
  [Simplify.]
Step: 3
So, the distance between the points A and D is 4 units.
Correct Answer is :   4 units
Q10On Sunday, Naomi went to Play Zone Park. At first she played at the Rope Climb. After sometime she moved to the Snack Bar. Which of the following represents the possible path from Rope Climb to Snack Bar?


A. move 3 units east and 2 units north
B. move 2 units north and 2 units east
C. move 2 units south and 2 units east
D. move 2 units north and 3 units east

Solutions
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Step: 1
By observing the chart, if Naomi starts from the Rope Climb and moves 2 units north and 2 units east, she will be at the Snack Bar.
Correct Answer is :   move 2 units north and 2 units east
Q11Barbara made a grid to show the location of the boating club to her friend. Which of the following shows the possible path from the play ground to the boating club?

A. move 5 units east and 5 units south
B. move 3 units south and 2 units west
C. move 4 units west and 4 units north
D. move 4 units east and 5 units north

Solutions
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Step: 1
As observed from the grid drawn by Barbara, her friend can reach the boating club if she moves 3 units to the south and 2 units to the west from the play ground.
Correct Answer is :   move 3 units south and 2 units west

HighSchool Math