Distance and Midpoint Lesson: Definitions, Formulas, and Examples

Lesson Overview

• Distance and Midpoints Definition
• Distance and Midpoints Formula
• Distance and Midpoints in the Coordinate Plane
• Solved Examples of Midpoints and Distance
• Distance and Midpoints Assessment

Distance and Midpoints Definition

Distance is the amount of space between two points. Think of it as the length of a straight line that connects two points.

• Example: If you are standing at point A and your friend is at point B, the distance is how far you would need to walk in a straight line to reach your friend.

The midpoint is the exact middle point between two points on a line. It is like cutting the distance in half and finding the center.

Example: If you and your friend are on opposite ends of a seesaw, the midpoint is the exact balance point in the center of the seesaw.

Distance and Midpoints Formula

Distance Formula

The distance formula helps us calculate the space between two points in a straight line. It is like using a ruler but for points on a graph.

Explanation:
This formula is based on the Pythagorean Theorem. It measures the hypotenuse of a right triangle, where the two legs are the differences in the x-coordinates and y-coordinates of the points.

Example:
Points: (1, 2) and (4, 6)

The distance is 5 units.

Midpoint Formula

The midpoint formula finds the middle point between two points on a line segment. It is like finding the average of the x and y coordinates.

Explanation:
The midpoint formula averages the x-values and y-values separately to find the center point between the two given points.

Example:
Points: (2, 3) and (6, 7)

The midpoint is (4, 5).

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Distance and Midpoint Quiz: Trivia Test!

Distance and Midpoints in the Coordinate Plane

Coordinate Plane: It has an x-axis and a y-axis.

Use the formulas to calculate the distance and midpoint between two points on the grid.

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Distance and Midpoint Test! Math Trivia Questions Quiz

Solved Examples of Midpoints and Distance

Example 1: What is the distance and midpoint between A(2, 3) and B(6, 7)?

Fig: Graphical representation of distance and midpoint between A(2, 3) and B(6, 7)

Example 2: What is the distance and midpoint between C(-3, 4) and D(1, -2)?

Fig: Graphical representation of distance and midpoint betweenC(-3, 4) and D(1, -2)

Example 3: What is the distance and midpoint between E(0, 0) and F(5, 12)?

Fig: Graphical representation of distance and midpoint between E(0, 0) and F(5, 12)

Example 4: What is the distance and midpoint between G(-7, -3) and H(-2, -6)?

Fig: Graphical representation of distance and midpoint between G(-7, -3) and H(-2, -6)

Example 5: What is the distance and midpoint between I(8, 2) and J(3, 10)?

Fig: Graphical representation of distance and midpoint between I(8, 2) and J(3, 10)

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Distance Formula quiz question

Distance and Midpoints Assessment

1. Find the distance between P(2, 3) and Q(6, 7).
2. Find the midpoint of R(-1, 5) and S(3, -3).
3. Solve: Is the distance between A(0, 0) and B(3, 4) equal to 5? Show your work.
4. Calculate the distance between X(-4, -2) and Y(2, 3).
5. Determine the midpoint of C(-5, -1) and D(5, 7).

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Frank Math 2 Distance and Midpoint