# Lesson Worksheet: Distance on the Coordinate Plane: Pythagorean Formula Mathematics • 8th Grade

In this worksheet, we will practice finding the distance between two points on the coordinate plane using the Pythagorean theorem.

Q1:

Find the distance between the point and the point of origin.

• A length units
• B length units
• C length units
• D length units

Q2:

Find the distance between the points and . • A4 length units
• B16 length units
• C length units
• D length units
• E length units

Q3:

Which of the following points is at a distance of from the origin?

• A
• B
• C
• D

Q4:

The coordinates of the points , , and are , , and respectively. Given that , find all possible values of .

• A or
• B or
• C or
• D or

Q5:

The distance between and is 5. What are the possible values of ?

• A or
• B or 4
• C or 4
• D or

Q6:

If and , where length units, find all the possible values of .

• A or
• B or
• C or
• D or

Q7:

What is the kind of triangle that the points , , and form with respect to its sides?

• AScalene triangle
• BEquilateral triangle
• CIsosceles triangle

Q8:

Point is on the circle with center . Decide whether point is on, inside, or outside the circle.

• AOutside the circle
• BInside the circle
• COn the circle

Q9:

Given , , and , what is the perimeter of ?

• A
• B
• C
• D18

Q10:

James is making a map of his local area measured in meters. The coffee shop is at and the Italian restaurant is at . Find the distance between the coffee shop and the Italian restaurant giving the answer to one decimal place.

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