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 ________________.