Constructing Perpendiculars: Shortest Distance to a Point

Learn how to find the shortest distance from a point to a line, ensuring the path taken is efficient and direct. By constructing a perpendicular from the point to the line, you guarantee the shortest possible route, creating a right angle with the line. Explore the process of constructing perpendiculars visually to understand why this method yields the shortest distance.

• Perpendicular Construction
• Shortest Distance
• Geometry Concepts
• Right Angle

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Uploaded on Aug 07, 2024 | 2 Views

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1. John is now standing at the point marked with a red cross. He wants to walk the shortest possible distance to the hedge. Where should John walk? X

2. Why wouldnt John walk this way to the hedge? X

3. How can we guarantee that we have drawn the shortest possible distance? X

4. The shortest possible route makes a right angle with the hedge X

5. This type of construction is referred as a perpendicular from a point.

6. When constructing a perpendicular from a point the new path is the shortest possible distance from the point to the line

7. Constructing a Perpendicular from a Point M P Q

8. Constructing a perpendicular from a point How can we show that the new line is the shortest possible distance from the point M to the line PQ? M P Q

9. Constructing a perpendicular from a point M P Q Measure it!

10. Constructing a Perpendicular from a Point M P Q

11. Constructing a Perpendicular from a Point M P Q Would this line be shorter?

12. Constructing a Perpendicular from a Point M P Q Why not?

13. The Perpendicular From a Point Construct the perpendicular from each of the given points on the worksheet. Complete your constructions on the worksheet Leave in your construction lines

14. Construct a perpendicular from a point on the following:

15. Construct a perpendicular from a point on the following:

16. Construct a perpendicular from a point on the following:

17. Challenge: Construct a line perpendicular to AB that passes through P Construct a line perpendicular to CD that passes through P What is the name of the resulting quadrilateral? Measure its side lengths with a ruler and calculate its area and perimeter