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Lesson 6.2 – The Distance Formula

Lesson 6.2 – The Distance Formula. Distance in the Coordinate Plane. Concept:. How do we find distances in the coordinate plane? (G.GPE.7). EQ:. Vocabulary:. Pythagorean Theorem Distance formula Square root Squared. H ow far apart are the points (-4, 1) and (2, 4)?. Activator. (2, 4).

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Lesson 6.2 – The Distance Formula

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  1. Lesson 6.2 – The Distance Formula Distance in the Coordinate Plane Concept: How do we find distances in the coordinate plane? (G.GPE.7) EQ: Vocabulary: Pythagorean Theorem Distance formula Square root Squared

  2. How far apart are the points (-4, 1) and (2, 4)? Activator (2, 4) (-4, -1)

  3. The Pythagorean Theorem c b a a2 + b2 = c2

  4. If you are given two points on a plane, you can draw a right triangle with the points as vertices. (2, 4) (-4, -1)

  5. Find the third vertex using your two points. Then find the vertical and horizontal distances. (2, 4) 5 6 (2, -1) (-4, -1)

  6. Once you have your horizontal and vertical distances, you can apply the Pythagorean Theorem. a2 + b2 = c2 c 62 + 52 = c2 b=5 36 + 25 = c2 a=6 c2 = 61 c =

  7. If you use variables in place of real values, you can derive a formula to calculate the distance between any two points. (x1, y1) (x2, y2) (x1, y2)

  8. To find the horizontal and vertical distances, find the differences between the x and y values respectively. This is called the Distance Formula. (x1, y1) c b a (x2, y2) (x1, y2)

  9. Use the distance formula to find the distance between the two given points. (2, 4) x1 = 2, y1 = 4 x2 = -4, y2 = -1 (-4, -1)

  10. The Distance Formula is a formula that allows you to find the distance between two points on a coordinate plane.

  11. Steps to using the Distance Formula: • Label the points ( and . • Write the Distance formula. • Substitute your points into the Distance Formula. • Evaluate using your calculator.

  12. Guided Practice - Example 1 Find the distance between the two points (2, 3) and (4, 5) *Round the result to the nearest hundredth if necessary.

  13. Guided Practice - Example 2 Find the distance between the two points (0, 4) and (-3, 0) *Round the result to the nearest hundredth if necessary.

  14. You Try - 1 Find the distance between the two points (-4, 2) and (1, 4) *Round the result to the nearest hundredth if necessary.

  15. Applying the Distance Formula • When applying the distance formula, directions are often used to describe the location of a point.

  16. Guided Practice - Example 3 From your home, you ride your bicycle 5 miles north, then 12 miles east. How far are you from your home?   • Prior to Step 1: Write your points based on the direction. • 5 miles north: x or y = ______ 12 miles east: x or y = ______ ( _____, _____ ) (Circle one) (Circle one) • Home: ( _____, _____ )

  17. Guided Practice - Example 3 From your home, you ride your bicycle 5 miles north, then 12 miles east. How far are you from your home? You are ________ miles from your home.

  18. Guided Practice - Example 4 Plane 1 is located six miles east and two miles south of an airport. Plane 2 is located one mile east and 10 miles north of the same airport. Find the distance between the planes. • Prior to Step 1: Write your points based on the direction. • Plane 1: 6 miles east: x or y = ______ ; 2 miles south: x or y = ______ ( _____, _____ ) • Plane 2: 1 mile east: x or y = ______ ; 10 miles north: x or y = ______ ( _____, _____ ) Circle one Circle one Circle one Circle one

  19. Guided Practice - Example 4 Plane 1 is located six miles east and two miles south of an airport. Plane 2 is located one mile east and 10 miles north of the same airport. Find the distance between the planes.  The planes are ________ miles apart.

  20. You Try 2 At a state park, Fred and Ben’s campsite is located three miles west and six miles north of the ranger station. Lizzie and Roxy’s campsite is located four miles east and two miles south of the ranger station. Find the distance between the campsites. • Prior to Step 1: Write your points based on the direction. • Fred and Ben’s Campsite: 3 miles west: x or y = ______ ; 6 miles north: x or y = ______ ( _____, _____ ) • Lizzie and Roxy’s Campsite: 4 miles east: x or y = ______ ; 2 miles south: x or y = ______ ( _____, _____ ) Circle one Circle one Circle one Circle one

  21. You Try 2 At a state park, Fred and Ben’s campsite is located three miles west and six miles north of the ranger station. Lizzie and Roxy’s campsite is located four miles east and two miles south of the ranger station. Find the distance between the campsites.  The campsites are ________ miles apart.

  22. On a sheet of paper, write down three things you learned today. Out of those three, write which one is most important and why. The Important Thing

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