ATL 02 - Using Logic to Make Geometric Deductions

Last updated over 4 years ago

7 questions

Note from the author:

Instructions

ATL 02 - Using Logic to Make Geometric Deductions

Last updated over 4 years ago

7 questions

Note from the author:

Distance between a point and a line #CriterionB 

Instructions

skills: Communication
strand: Make inferences and draw conclusions
Rubric: 
BE - 7/14
AE - 9/14
ME - 11/14
EE - 13/14

The diagram shows point A (4,7).
Write down the distance from point A to the x-axis.

Billy says, 'The point B(2,0) lies on the x-axis. Pythagoras' theorem tells me that the distance from A to B is units.
Therefore the distance from A to x-axis is \sqrt{53} = 7.3 units.'
Explain whether or not this is a logical argument.

Sketch the line y=5 on the diagram.
Write down the distance from A to the line y=5.

Sketch the line x=1 on the diagram.
Choose a point on the line x=1 that is closest to point A.
What is the distance from A to line x=1?

Sketch the line y=x+1 on the diagram.
Choose a point on the line y=x+1 that is closest to point A.
What is the distance from A to line y=x+1?

https://www.geogebra.org/classic/dskgrhcp
By using the link to the Geogebra, drag point B along the line y=7-2x.
What is the shortest distance from point A to the line y=7-2x

ATL 02 - Using Logic to Make Geometric Deductions

ATL 02 - Using Logic to Make Geometric Deductions

The diagram shows point A (4,7).
Write down the distance from point A to the x-axis.

Billy says, 'The point B(2,0) lies on the x-axis. Pythagoras' theorem tells me that the distance from A to B is units.
Therefore the distance from A to x-axis is \sqrt{53} = 7.3 units.'
Explain whether or not this is a logical argument.

Sketch the line y=5 on the diagram.
Write down the distance from A to the line y=5.

Sketch the line x=1 on the diagram.
Choose a point on the line x=1 that is closest to point A.
What is the distance from A to line x=1?

Sketch the line y=x+1 on the diagram.
Choose a point on the line y=x+1 that is closest to point A.
What is the distance from A to line y=x+1?

https://www.geogebra.org/classic/dskgrhcp
By using the link to the Geogebra, drag point B along the line y=7-2x.
What is the shortest distance from point A to the line y=7-2x

Conclusion:
The shortest distance between a given line (let's say line L) and a point not on line L is measured along ________________.

The diagram shows point A (4,7).
Write down the distance from point A to the x-axis.

Billy says, 'The point B(2,0) lies on the x-axis. Pythagoras' theorem tells me that the distance from A to B is units.
Therefore the distance from A to x-axis is \sqrt{53} = 7.3 units.'
Explain whether or not this is a logical argument.

Sketch the line y=5 on the diagram.
Write down the distance from A to the line y=5.

Sketch the line x=1 on the diagram.
Choose a point on the line x=1 that is closest to point A.
What is the distance from A to line x=1?

Sketch the line y=x+1 on the diagram.
Choose a point on the line y=x+1 that is closest to point A.
What is the distance from A to line y=x+1?

https://www.geogebra.org/classic/dskgrhcp
By using the link to the Geogebra, drag point B along the line y=7-2x.
What is the shortest distance from point A to the line y=7-2x

Conclusion:
The shortest distance between a given line (let's say line L) and a point not on line L is measured along ________________.

ATL 02 - Using Logic to Make Geometric Deductions

ATL 02 - Using Logic to Make Geometric Deductions

The diagram shows point A (4,7).Write down the distance from point A to the x-axis.

Billy says, 'The point B(2,0) lies on the x-axis. Pythagoras' theorem tells me that the distance from A to B is units.Therefore the distance from A to x-axis is \sqrt{53} = 7.3 units.'Explain whether or not this is a logical argument.

Sketch the line y=5 on the diagram. Write down the distance from A to the line y=5.

Sketch the line x=1 on the diagram. Choose a point on the line x=1 that is closest to point A.What is the distance from A to line x=1?

Sketch the line y=x+1 on the diagram. Choose a point on the line y=x+1 that is closest to point A.What is the distance from A to line y=x+1?

https://www.geogebra.org/classic/dskgrhcpBy using the link to the Geogebra, drag point B along the line y=7-2x. What is the shortest distance from point A to the line y=7-2x

Conclusion:The shortest distance between a given line (let's say line L) and a point not on line L is measured along ________________.

The diagram shows point A (4,7).Write down the distance from point A to the x-axis.

Billy says, 'The point B(2,0) lies on the x-axis. Pythagoras' theorem tells me that the distance from A to B is units.Therefore the distance from A to x-axis is \sqrt{53} = 7.3 units.'Explain whether or not this is a logical argument.

Sketch the line y=5 on the diagram. Write down the distance from A to the line y=5.

Sketch the line x=1 on the diagram. Choose a point on the line x=1 that is closest to point A.What is the distance from A to line x=1?

Sketch the line y=x+1 on the diagram. Choose a point on the line y=x+1 that is closest to point A.What is the distance from A to line y=x+1?

https://www.geogebra.org/classic/dskgrhcpBy using the link to the Geogebra, drag point B along the line y=7-2x. What is the shortest distance from point A to the line y=7-2x

Conclusion:The shortest distance between a given line (let's say line L) and a point not on line L is measured along ________________.

The diagram shows point A (4,7).
Write down the distance from point A to the x-axis.

Billy says, 'The point B(2,0) lies on the x-axis. Pythagoras' theorem tells me that the distance from A to B is units.
Therefore the distance from A to x-axis is \sqrt{53} = 7.3 units.'
Explain whether or not this is a logical argument.

Sketch the line y=5 on the diagram.
Write down the distance from A to the line y=5.

Sketch the line x=1 on the diagram.
Choose a point on the line x=1 that is closest to point A.
What is the distance from A to line x=1?

Sketch the line y=x+1 on the diagram.
Choose a point on the line y=x+1 that is closest to point A.
What is the distance from A to line y=x+1?

https://www.geogebra.org/classic/dskgrhcp
By using the link to the Geogebra, drag point B along the line y=7-2x.
What is the shortest distance from point A to the line y=7-2x

Conclusion:
The shortest distance between a given line (let's say line L) and a point not on line L is measured along ________________.

The diagram shows point A (4,7).
Write down the distance from point A to the x-axis.

Billy says, 'The point B(2,0) lies on the x-axis. Pythagoras' theorem tells me that the distance from A to B is units.
Therefore the distance from A to x-axis is \sqrt{53} = 7.3 units.'
Explain whether or not this is a logical argument.

Sketch the line y=5 on the diagram.
Write down the distance from A to the line y=5.

Sketch the line x=1 on the diagram.
Choose a point on the line x=1 that is closest to point A.
What is the distance from A to line x=1?

Sketch the line y=x+1 on the diagram.
Choose a point on the line y=x+1 that is closest to point A.
What is the distance from A to line y=x+1?

https://www.geogebra.org/classic/dskgrhcp
By using the link to the Geogebra, drag point B along the line y=7-2x.
What is the shortest distance from point A to the line y=7-2x

Conclusion:
The shortest distance between a given line (let's say line L) and a point not on line L is measured along ________________.