The Coordinate Plane: Lesson 3 - Slope and Distance

Slope and Distance is the third of four self-paced lessons in the “The Coordinate Plane” section of KET’s GED^{®} Geometry Professional Development Online Course. This lesson focuses on applying previously-learned concepts about the coordinate plane, using the formulas for slope and distance.

NOTE: This course was created based on the 2002 GED^{®} math test. The geometry instruction in this course is still valid, however, for up-to-date information about the 2014 GED^{®} math test, please visit KET’s GED^{®} Test Info: Mathematics online course.

On the GED^{®} Mathematics Test, students need to answer questions that require them to work with a number of relationships on the coordinate plane.

They need to be able to find the slope of a graphed line.

They also need to find the distance between two plotted points.

This lesson focuses on students applying what they have learned about the coordinate plane. They will need to use the formulas page to find the formula for slope and the formula for the distance between two points. They also will need to understand operations with signed numbers and finding the square root as a prerequisite for these skills.

2Slope

Watch the video to learn how to how to find and determine slope.

Slope

Video: 0m 28s

Slope is the measure of the incline, or steepness, of a line on the coordinate plane. Slope is a ratio that compares the rise (change up or down) to the run (change left or right). The slope formula is on the GED formulas page under “Coordinate Geometry.”

If a line moves up from left to right, the slope is positive. If a line moves down from left to right, the slope is negative.

The slope of a horizontal line is 0. The slope of a vertical line is undefined, meaning it cannot be measured.

Question Find the slope of a line that passes through the points (–4, 6) and (6, 1). Is the slope positive or negative?

Step 1 Choose one point for (x_{1}, y_{1}) and the other for (x_{2}, y_{2}).

Step 2 Use the slope formula. Substitute the values and simplify. The slope is negative so the line slopes downward from left to right.

Answer

3Distance Between Two Points

Finding the distance between two points depends on the type of line that contains the points.

If two points are on the same horizontal or vertical line, count the units. In the grid below, the distance from A to B is 6 units. From C to B is 8 units.

If two points are on a slanted line, such as A to C on the grid above, use the distance between points formula under “Coordinate Geometry” on the GED formulas page.

Question The coordinates of two points are (6, 4) and (2, 1). What is the distance between the points?

Step 1 Choose one point for (x_{1}, y_{1}) and the other for (x_{2}, y_{2}).

Step 2 Use the distance formula. Substitute the values and simplify.

d = √(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

d = √(6 - 2)^{2} + (4 - 1)^{2} ← subtract inside parentheses first

d = √4^{2} + 3^{2}

d = √16 + 9 = √25 = 5 ← simplify

Answer 5 units

4Sample GED Questions

Directions: There are two questions on this page. Each will appear in the blue rectangle below. Click on Question 1 to see the first question, and then select your answer. Click on Question 2 to see the second question, and select your answer. As you solve these problems, consider how you would work through them with your students.

How could you help students find the two nearest whole numbers for √20 ?

The Coordinate Plane: Slope and Distance Skill Review

Document

Printable Resource

In this lesson you have learned about slope and distance. This review consists of key terms and concepts with which you will need to be familiar. Click the view button on the left to access a review sheet.

Below you will also see a Classroom Connection with suggestions for linking this geometry content with your instruction.