Mathematics
Grade 6
15 min
Distance between two points
Distance between two points
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify and plot points on a coordinate plane using ordered pairs.
Distinguish between horizontal and vertical line segments on a coordinate plane.
Calculate the horizontal distance between two points that share the same y-coordinate.
Calculate the vertical distance between two points that share the same x-coordinate.
Apply the concept of absolute value to find distances when coordinates have different signs.
Solve real-world problems involving distances between points on a grid.
Ever wondered how far apart two places are on a map? 🗺️ Today, we'll learn to measure distances on our own mathematical map called the coordinate plane!
In this lesson, you'll discover how to find the exact distance between any two points that are directly across from...
2
Key Concepts & Vocabulary
TermDefinitionExample
Coordinate PlaneA flat surface formed by two intersecting number lines (the x-axis and y-axis), used to locate points.Imagine a checkerboard; each square has a specific location that can be described on a coordinate plane.
X-axisThe horizontal number line on the coordinate plane.When you walk left or right, you're moving along the x-axis.
Y-axisThe vertical number line on the coordinate plane.When you walk up or down, you're moving along the y-axis.
OriginThe point where the x-axis and y-axis intersect, represented by the ordered pair (0,0).It's the starting point, like the center of a crosswalk where two streets meet.
Ordered PairA pair of numbers (x, y) that tells you the exact location of a point on the coordinate plane. The first number is the x-co...
3
Core Formulas
Horizontal Distance Rule
$$|x_2 - x_1|$$
Use this rule to find the distance between two points that are on the same horizontal line (they have the same y-coordinate). Subtract their x-coordinates and take the absolute value of the result.
Vertical Distance Rule
$$|y_2 - y_1|$$
Use this rule to find the distance between two points that are on the same vertical line (they have the same x-coordinate). Subtract their y-coordinates and take the absolute value of the result.
5 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
A rectangle has vertices at A(-4, 3), B(5, 3), C(5, -2), and D(-4, -2). What is the perimeter of the rectangle?
A.14 units
B.23 units
C.45 units
D.28 units
Challenging
A student says the distance between P(-3, 4) and Q(2, -1) can be found using |2 - (-3)| = 5. Why is this reasoning incorrect?
A.They subtracted the integers incorrectly.
B.The points do not share a coordinate, so a horizontal or vertical distance formula cannot be used.
C.They should have used the y-coordinates instead: |4 - (-1)| = 5.
D.They forgot to use absolute value.
Challenging
A square has vertices at (2, 1), (7, 1), (7, 6), and (x, y). What are the coordinates of the fourth vertex (x, y)?
A.(6, 2)
B.(7, 2)
C.(2, 6)
D.(6, 7)
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing Free