Curriculum / Math / 8th Grade / Unit 7: Pythagorean Theorem and Volume / Lesson 12
Math
Unit 7
8th Grade
Lesson 12 of 16
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Find the distance between points in the coordinate plane using the Pythagorean Theorem.
The core standards covered in this lesson
8.G.B.8 — Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
The foundational standards covered in this lesson
6.G.A.3 — Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Three line segments are shown in the coordinate plane below. Order the line segments from shortest to longest.
A triangle is defined by the following vertices in the coordinate plane:
$${A: \space (-3,5)}$$, $${B: \space (2,7)}$$, $${C: \space (-3,-1)}$$
Find the perimeter of the triangle to the nearest tenth of a unit. You may use the grid below if needed.
The line segments in the list below are defined by the pairs of coordinate points shown.
$${\overline{AB}}$$: (1, 4) and (4, 7) $${\overline{CD}}$$: (2, 2) and (5, 0) $${\overline{EF}}$$: (6, 0) and (7, 4) $${\overline{GH}}$$: (3, 4) and (9, 7) $${\overline{IJ}}$$: (12, 1) and (7, 5) $${\overline{KL}}$$: (1, 2) and (5, 4)
a. Pick one pair of points. Plot the points on a coordinate grid and find the exact distance between the points. Describe how you find the distance.
b. Pick another pair of points. Find the exact distance between the points without plotting them on a coordinate plane. You can check your answer on a coordinate plane afterward.
A set of suggested resources or problem types that teachers can turn into a problem set
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Line segment $${\overline{JK}}$$ is defined by the points $${J \space (-5,1)}$$ and $${K \space (-5,8)}$$. Line segment $${\overline{AB}}$$ is shown below.
Which line segment is longer?
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The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 11
Lesson 13
Topic A: Irrational Numbers and Square Roots
Define, evaluate, and estimate square roots.
8.EE.A.2
Understand that some numbers, including $${\sqrt{2}}$$, are irrational. Approximate the value of irrational numbers.
8.NS.A.1 8.NS.A.2
Locate irrational values approximately on a number line. Compare values of irrational numbers.
8.NS.A.2
Represent rational numbers as decimal expansions.
8.NS.A.1
Represent decimal expansions as rational numbers in fraction form.
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Topic B: Understanding and Applying the Pythagorean Theorem
Understand the Pythagorean Theorem as a relationship between the side lengths in a right triangle.
8.G.B.6
Understand a proof of the Pythagorean Theorem.
Use the converse of the Pythagorean Theorem to determine if a triangle is a right triangle.
Find missing side lengths involving right triangles and apply to area and perimeter problems.
8.G.B.7
Solve real-world and mathematical problems using the Pythagorean Theorem (Part I).
Solve real-world and mathematical problems using the Pythagorean Theorem (Part II).
8.G.B.8
Topic C: Volume and Cube Roots
Define and evaluate cube roots. Solve equations in the form $${x^2=p}$$ and $${x^3=p}$$.
8.EE.A.2 8.NS.A.2
Solve real-world and mathematical problems involving the volume of cylinders and cones.
8.G.C.9
Solve real-world and mathematical problems involving the volume of spheres.
Solve real-world problems involving multiple three-dimensional shapes, in particular, cylinders, cones, and spheres.
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