Spectrum Math Grade 8 Chapter 5 Lesson 9 Answer Key Pythagorean Theorem in the Coordinate Plane

Students can use the Spectrum Math Grade 8 Answer Key Chapter 5 Lesson 5.9 Pythagorean Theorem in the Coordinate Plane as a quick guide to resolve any of their doubts.

Spectrum Math Grade 8 Chapter 5 Lesson 5.9 Pythagorean Theorem in the Coordinate Plane Answers Key

The Pythagorean Theorem can be used to find an unknown distance between two points on a coordinate plane.
Find the distance between points A and B.
Step 1: Draw lines extending from points A and B so that when they intersect they create a right angle. Label the point at which they meet, point C.

Step 2: Find the distance of segment \(\overline{A C}\) (7), and segment \(\overline{B C}\) (6).
Step 3: Use Pythagorean Theorem to find the length of segment \(\overline{A B}\).
7² + 6² = 85
(\(\overline{A B}\))² = 85
\(\overline{A B}\) = \(\sqrt{85}\) = 9.22

Find the distance between each of the points given below using the Pythagorean Theorem. Round answers to the nearest hundredth.

Question 1.
a.

\(\overline{C D}\) = ________
Answer: \(\overline{C D}\) = 12.52

The Pythagorean Theorem can be used to find an unknown distance between two points on a coordinate plane.
Step 1: Draw lines extending from points A and B so that when they intersect they create a right angle. Label the point at which they meet, point E.
Step 2: Find the distance of segment \(\overline{DE}\) (11), and segment \(\overline{CE}\) (6).
Step 3: Use Pythagorean Theorem to find the length of segment \(\overline{CD}\).
11² + 6² = 157
(\(\overline{CD}\))² = 157
\(\overline{CD}\) = \(\sqrt{157}\) = 12.52

b.

\(\overline{E F}\) = ________
Answer: \(\overline{E F}\) = 10.19

The Pythagorean Theorem can be used to find an unknown distance between two points on a coordinate plane.
Step 1: Draw lines extending from points A and B so that when they intersect they create a right angle. Label the point at which they meet, point D.
Step 2: Find the distance of segment \(\overline{DE}\) (10), and segment \(\overline{FD}\) (2).
Step 3: Use Pythagorean Theorem to find the length of segment \(\overline{CD}\).
10² + 2² = 104
(\(\overline{EF}\))² = 104
\(\overline{EF}\) = \(\sqrt{104}\) = 10.19

c.

\(\overline{G H}\) = ________
Answer: \(\overline{G H}\) = 9.433

The Pythagorean Theorem can be used to find an unknown distance between two points on a coordinate plane.
Step 1: Draw lines extending from points A and B so that when they intersect they create a right angle. Label the point at which they meet, point I.
Step 2: Find the distance of segment \(\overline{GI}\) (8), and segment \(\overline{HI}\) (5).
Step 3: Use Pythagorean Theorem to find the length of segment \(\overline{GH}\).
8² + 5² = 89
(\(\overline{GH}\))² = 89
\(\overline{GH}\) = \(\sqrt{89}\) = 9.433

Question 2.
a.

\(\overline{C D}\) = ________
Answer: \(\overline{C D}\) = 13.416

The Pythagorean Theorem can be used to find an unknown distance between two points on a coordinate plane.
Step 1: Draw lines extending from points A and B so that when they intersect they create a right angle. Label the point at which they meet, point E.
Step 2: Find the distance of segment \(\overline{DE}\) (6), and segment \(\overline{CE}\) (12).
Step 3: Use Pythagorean Theorem to find the length of segment \(\overline{CD}\).
6² + 12² = 180
(\(\overline{CD}\))² = 180
\(\overline{CD}\) = \(\sqrt{180}\) = 13.416

b.

\(\overline{E F}\) = ________
Answer: \(\overline{E F}\) = 12.165

The Pythagorean Theorem can be used to find an unknown distance between two points on a coordinate plane.
Step 1: Draw lines extending from points A and B so that when they intersect they create a right angle. Label the point at which they meet, point D.
Step 2: Find the distance of segment \(\overline{DE}\) (12), and segment \(\overline{FD}\) (2).
Step 3: Use Pythagorean Theorem to find the length of segment \(\overline{EF}\).
2² + 12² = 148
(\(\overline{EF}\))² = 148
\(\overline{EF}\) = \(\sqrt{148}\) = 12.165

c.

\(\overline{G H}\) = ________
Answer: \(\overline{G H}\) = 12.369

The Pythagorean Theorem can be used to find an unknown distance between two points on a coordinate plane.
Step 1: Draw lines extending from points A and B so that when they intersect they create a right angle. Label the point at which they meet, point I.
Step 2: Find the distance of segment \(\overline{HI}\) (12), and segment \(\overline{GI}\) (3).
Step 3: Use Pythagorean Theorem to find the length of segment \(\overline{EF}\).
3² + 12² = 153
(\(\overline{GH}\))² = 153
\(\overline{GH}\) = \(\sqrt{153}\) = 12.369

Find the distance between each of the points given below using the Pythagorean Theorem. Round answers to the nearest hundredth.

Question 1.
a.

\(\overline{C D}\) = ________
Answer: \(\overline{C D}\) = 9.85

The Pythagorean Theorem can be used to find an unknown distance between two points on a coordinate plane.
Step 1: Draw lines extending from points A and B so that when they intersect they create a right angle. Label the point at which they meet, point E.
Step 2: Find the distance of segment \(\overline{DE}\) (4), and segment \(\overline{CE}\) (9).
Step 3: Use Pythagorean Theorem to find the length of segment \(\overline{CD}\).
4² + 9² = 97
(\(\overline{CD}\))² = 97
\(\overline{CD}\) = \(\sqrt{97}\) = 9.8488 = 9.85

b.

\(\overline{E F}\) = ________
Answer: \(\overline{E F}\) = 8.54

The Pythagorean Theorem can be used to find an unknown distance between two points on a coordinate plane.
Step 1: Draw lines extending from points A and B so that when they intersect they create a right angle. Label the point at which they meet, point D.
Step 2: Find the distance of segment \(\overline{DE}\) (8), and segment \(\overline{FD}\) (3).
Step 3: Use Pythagorean Theorem to find the length of segment \(\overline{CD}\).
3² + 8² = 73
(\(\overline{EF}\))² = 73
\(\overline{EF}\) = \(\sqrt{73}\) = 8.544= 8.54

c.

\(\overline{G H}\) = ________
Answer: \(\overline{G H}\) = 9.9

The Pythagorean Theorem can be used to find an unknown distance between two points on a coordinate plane.
Step 1: Draw lines extending from points A and B so that when they intersect they create a right angle. Label the point at which they meet, point I.
Step 2: Find the distance of segment \(\overline{GI}\) (7), and segment \(\overline{HI}\) (7).
Step 3: Use Pythagorean Theorem to find the length of segment \(\overline{GH}\).
7² + 7² = 98
(\(\overline{GH}\))² = 98
\(\overline{GH}\) = \(\sqrt{98}\) = 9.899= 9.9

Question 2.
a.

\(\overline{P Q}\) = ________
Answer: \(\overline{P Q}\) =  9.05

The Pythagorean Theorem can be used to find an unknown distance between two points on a coordinate plane.
Step 1: Draw lines extending from points A and B so that when they intersect they create a right angle. Label the point at which they meet, point R.
Step 2: Find the distance of segment \(\overline{PR}\) (1), and segment \(\overline{RQ}\) (9).
Step 3: Use Pythagorean Theorem to find the length of segment \(\overline{GH}\).
9² + 1² =82
(\(\overline{PQ}\))² = 82
\(\overline{PQ}\) = \(\sqrt{82}\) = 9.055 = 9.05

b.

\(\overline{A B}\) = ________
Answer: \(\overline{A B}\) = 6.4

The Pythagorean Theorem can be used to find an unknown distance between two points on a coordinate plane.
Step 1: Draw lines extending from points A and B so that when they intersect they create a right angle. Label the point at which they meet, point C.
Step 2: Find the distance of segment \(\overline{AC}\) (5), and segment \(\overline{BC}\) (4).
Step 3: Use Pythagorean Theorem to find the length of segment \(\overline{GH}\).
5² + 4² =41
(\(\overline{AB}\))² = 41
\(\overline{AB}\) = \(\sqrt{41}\) = 6.403 = 6.4

c.

\(\overline{X Y}\) = ________
Answer: \(\overline{X Y}\) = 6.7

The Pythagorean Theorem can be used to find an unknown distance between two points on a coordinate plane.
Step 1: Draw lines extending from points A and B so that when they intersect they create a right angle. Label the point at which they meet, point Z.
Step 2: Find the distance of segment \(\overline{YZ}\) (3), and segment \(\overline{XZ}\) (6).
Step 3: Use Pythagorean Theorem to find the length of segment \(\overline{XY}\).
3² + 6² =45
(\(\overline{XY}\))² = 45
\(\overline{XY}\) = \(\sqrt{45}\) = 6.708 = 6.7

Question 3.
a.

\(\overline{T R}\) = ________
Answer: \(\overline{T R}\) = 8.54

The Pythagorean Theorem can be used to find an unknown distance between two points on a coordinate plane.
Step 1: Draw lines extending from points A and B so that when they intersect they create a right angle. Label the point at which they meet, point S.
Step 2: Find the distance of segment \(\overline{ST}\) (8), and segment \(\overline{RS}\) (3).
Step 3: Use Pythagorean Theorem to find the length of segment \(\overline{RT}\).
8² + 3² =73
(\(\overline{RT}\))² = 73
\(\overline{RT}\) = \(\sqrt{73}\) = 8.544 = 8.54

b.

\(\overline{B K}\) = ________
Answer: \(\overline{B K}\) = 8.60

The Pythagorean Theorem can be used to find an unknown distance between two points on a coordinate plane.
Step 1: Draw lines extending from points A and B so that when they intersect they create a right angle. Label the point at which they meet, point R.
Step 2: Find the distance of segment \(\overline{RK}\) (5), and segment \(\overline{RB}\) (7).
Step 3: Use Pythagorean Theorem to find the length of segment \(\overline{RT}\).
7² + 5² =74
(\(\overline{BK}\))² = 74
\(\overline{BK}\) = \(\sqrt{74}\) = 8.602 = 8.60

c.

\(\overline{J E}\) = ________
Answer: \(\overline{J E}\) = 8.48

The Pythagorean Theorem can be used to find an unknown distance between two points on a coordinate plane.
Step 1: Draw lines extending from points A and B so that when they intersect they create a right angle. Label the point at which they meet, point R.
Step 2: Find the distance of segment \(\overline{RE}\) (6), and segment \(\overline{RJ}\) (6).
Step 3: Use Pythagorean Theorem to find the length of segment \(\overline{RT}\).
6² + 6² =72
(\(\overline{EJ}\))² = 72
\(\overline{EJ}\) = \(\sqrt{72}\) = 8.485 = 8.48