ALEX Resources

   View Standards     Standard(s): [MA2019] REG-8 (8) 27 :

27. Apply the Pythagorean Theorem to find the distance between two points in a coordinate plane.

In this lesson, the teacher will demonstrate how to use the Pythagorean Theorem to find distance between two points in the coordinate system. In the coordinate plane, the difference in the x- and y-values will determine the numbers to calculate the distance. This lesson will use online graphing tools as well as graph paper to plot the points. This lesson can also be used to show the relationship between the distance formula and the Pythagorean Theorem.

This lesson results from the ALEX Resource Gap Project.

   View Standards     Standard(s): [MA2019] REG-8 (8) 9 :

9. Interpret y = mx + b as defining a linear equation whose graph is a line with m as the slope and b as the y-intercept.

a. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in a coordinate plane.

b. Given two distinct points in a coordinate plane, find the slope of the line containing the two points and explain why it will be the same for any two distinct points on the line.

c. Graph linear relationships, interpreting the slope as the rate of change of the graph and the y-intercept as the initial value.

d. Given that the slopes for two different sets of points are equal, demonstrate that the linear equations that include those two sets of points may have different y-intercepts.

[MA2019] REG-8 (8) 12 :

12. Solve systems of two linear equations in two variables by graphing and substitution.

a. Explain that the solution(s) of systems of two linear equations in two variables corresponds to points of intersection on their graphs because points of intersection satisfy both equations simultaneously.

b. Interpret and justify the results of systems of two linear equations in two variables (one solution, no solution, or infinitely many solutions) when applied to real-world and mathematical problems.

[MA2015] (8) 13 :

13 ) Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear. [8-F3]

Example: The function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4), and (3,9), which are not on a straight line.

[MA2019] REG-8 (8) 27 :

27. Apply the Pythagorean Theorem to find the distance between two points in a coordinate plane.

[MA2019] (6) 11 :

11. Find the position of pairs of integers and other rational numbers on the coordinate plane.

a. Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the x and y coordinates.

b. Identify (a,b) and (a,-b) as reflections across the x-axis.

c. Identify (a,b) and (-a,b) as reflections across the y-axis.

d. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding distances between points with the same first or second coordinate.

[MA2019] ACC-7 (7) 6 :

6. Interpret y = mx + b as defining a linear equation whose graph is a line with m as the slope and b as the y-intercept.

a. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in a coordinate plane.

b. Given two distinct points in a coordinate plane, find the slope of the line containing the two points and explain why it will be the same for any two distinct points on the line.

c. Graph linear relationships, interpreting the slope as the rate of change of the graph and the y-intercept as the initial value.

d. Given that the slopes for two different sets of points are equal, demonstrate that the linear equations that include those two sets of points may have different y-intercepts. [Grade 8, 9]

Students will create a map of a shopping excursion by solving systems of linear equations through graphing, substitution, or elimination. Students will then be able to determine the distance traveled through the mall using Pythagorean Theorem. Students will utilize previous grade level standards as a spiral review such as plotting coordinate pairs and using those pairs to find the distance between two points.

This activity is a result of the ALEX Resource Development Summit.

   View Standards     Standard(s): [MA2019] REG-8 (8) 27 :

27. Apply the Pythagorean Theorem to find the distance between two points in a coordinate plane.

[MA2019] ACC-8 (8) 49 :

49. Apply the Pythagorean Theorem to find the distance between two points in a coordinate plane. [Grade 8, 27]

Discover how math is required for quality construction when a Master Carpenter shares his experience and expertise. This video focuses on explaining slope as rise over run and shows how slope comes into play when building homes to take math out of the classroom and into real world problem solving. This resource is part of the Math at the Core: Middle School collection.

   View Standards     Standard(s): [MA2019] REG-8 (8) 27 :

27. Apply the Pythagorean Theorem to find the distance between two points in a coordinate plane.

[MA2019] ACC-8 (8) 49 :

49. Apply the Pythagorean Theorem to find the distance between two points in a coordinate plane. [Grade 8, 27]

In this video, learn how using the Pythagorean Theorem can help people solve real-world problems involving distances. In the accompanying classroom activity, students develop their problem-solving, spatial reasoning, and geometry skills by putting the Pythagorean Theorem to use. After a brief discussion about how to use the theorem to find the distance between two points on a coordinate grid, students partner up and play a game in which they generate (and then calculate the distance between) two or more points on the grid. As the game increases in complexity, students begin working in all quadrants and begin identifying multiple triangles that they can use to determine the distance between points.

   View Standards     Standard(s): [MA2019] REG-8 (8) 26 :

26. Informally justify the Pythagorean Theorem and its converse.

[MA2019] REG-8 (8) 27 :

27. Apply the Pythagorean Theorem to find the distance between two points in a coordinate plane.

[MA2019] REG-8 (8) 28 :

28. Apply the Pythagorean Theorem to determine unknown side lengths of right triangles, including real-world applications

Module 7, Topic C revisits the Pythagorean Theorem and its applications, now in a context that includes the use of square roots and irrational numbers. Students learn another proof of the Pythagorean Theorem involving areas of squares off of each side of a right triangle (8.G.B.6). Another proof of the converse of the Pythagorean Theorem is presented to students, which requires an understanding of congruent triangles (8.G.B.6). With the concept of square roots firmly in place, students apply the Pythagorean Theorem to solve real-world and mathematical problems to determine an unknown side length of a right triangle and the distance between two points on the coordinate plane (8.G.B.7, 8.G.B.8).