# Lesson Worksheet: Distance on the Coordinate Plane: Horizontal and Vertical Mathematics • 6th Grade

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

Q1:

Find the length of . Q2:

Find the lengths of and , where the coordinates of points , , , and are , , , and , respectively, considering that a length unit is equal to 1 cm. • A,
• B,
• C,
• D,

Q3:

Given points and , calculate the distance between the two points, and , considering that a length unit .

Q4:

Use the graph below to determine the points , , , and , and find the area of the shape that results from connecting them. • A, , , , 48
• B, , , , 96
• C, , , , 48
• D, , , , 96

Q5:

If is a square, where , , , and , find the ordered pair that represents and then determine the area of the square considering a unit length . • A, area
• B, area
• C, area
• D, area

Q6:

Use the graph below to determine the coordinates of the points , , and , then find the area of the resulting figure from connecting the points. • A, , , 20 area units
• B, , , 20 area units
• C, , , 10 area units
• D, , , 10 area units

Q7:

Given that one length unit equals 1 cm, find the perimeter of , where the coordinates of points , , , and are , , , and , respectively. Q8:

Do the two points and lie on the same side of the line ?

• AYes
• BNo

Q9:

What is the distance between the points and ?

Q10:

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

• BDavid

Q11:

David and James are two friends who go to the same school. David’s room is located at , James’s room at , and the band room at .

How far is David’s room from James’s?

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

Q12:

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 , the river at , the tent at , and the big tree at .

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?

Q13:

Suppose that in the given figure, and is on the . What is the length of ? Q14:

Find the length of the base of Triangle B. Q15:

Anthony graphed the points and . He said that the distance between these points is 4. Do you agree or disagree?

• Bagree

Q16:

Find the distance between point , located at , and point , located at .

Q17:

What is the distance between the point and the -axis?

Q18:

Given that the coordinates of the points and are and respectively, and one unit length , find the length of .

Q19:

Given that the coordinates of and are and , respectively, determine the length of .

• A8 length units
• B3 length units
• C16 length units
• D6 length units

Q20:

Point is located at . Which of the following points is 6 units away from point ?

• A
• B
• C
• D
• E

Q21:

To go to the park from the mall, a straight path is taken which can be represented on a coordinate grid by the points and .

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

• A • B • C • D • E Find the distance between and .

Q22:

In a coordinate plane, David’s middle school lies at and his elementary school at . Each unit in the plane represents 1 mile in reality. If David 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?

Q23:

Are the points , , and collinear?

• AYes
• BNo

Q24:

Given that the coordinates of points and are and respectively, find the perimeter of the figure . Q25:

A farmer wants to build a metal fence to enclose his livestock. The fence’s vertices are represented by points , , , , , and . Each unit in the coordinate plane represents 1 meter in reality. Since a gate is to be added between points and , the farmer will not use metal fencing on that side. What is the total number of meters of metal fencing the farmer needs?