Co-ordinate Geometry: Verify that 3x - y - 4 = 0 contains pt (2, 2). Hence find shortest distance between line and 6x - 2y + 7 = 0

[reggiwilliams]

Came across this question when revising Co-ordinate geometry
Have tried doing but not sure if my answer is correct
Attach question and my workings

 

[Dr.Peterson]

Came across this question when revising Co-ordinate geometry
Have tried doing but not sure if my answer is correct
Attach question and my workings

Yes, your answer is correct. I would have been easier to determine that if you had included all the work in the image, rather than cropping too tightly and losing words.

I checked by using another method, determining the distance of each line from the origin. Your work is likely what was expected.

 

[reggiwilliams]

Yes, your answer is correct. I would have been easier to determine that if you had included all the work in the image, rather than cropping too tightly and losing words.

I checked by using another method, determining the distance of each line from the origin. Your work is likely what was expected.

Here are my workings

 

[The Highlander]

Came across this question when revising Co-ordinate geometry
Have tried doing but not sure if my answer is correct
Attach question and my workings

Hi Reggie,

I'm sorry but trying to decipher your (original) workings was making my brain hurt so I just did it myself and got (pretty much) the same answer as you.

It's always helpful to start off with a diagram such as this...

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Having determined the equation of a line at right angles to the green one I then solved the (red & black) equations simultaneously to get the point of intersection between the red & black lines as (2.25, 2.75), then, using the distance formula, I got the distance between (0, 3.5) and (2.25, 2.75) to be (approximately) 2.3717 units.

Hope that helps.