Help with question please 2U Fitzpatrick! (1 Viewer)

[yoloswag]

Some of you might remember this from New Senior Maths 2U.

The question is:

Find the equation of the locus that is subject to: the distance of a point from the line x=4 is equal to the distance from the line y=1.

The second question:

Find the equation of the locus from the line x=-3 which is two fifths of its distance from the line y=-1.

Last question:

A point root 2 units from the line with equation y=x.

Any help would be gladly appreicated!!!!

 

[braintic]

(1) The distance of any point (x,y) from the line x=4 is |x-4|.
Similarly, the distance of any point (x,y) from the line y=1 is |y-1|.
So, |x-4|=|y-1|
x-4=y-1 or x-4 = 1-y
x-y=3, x+y=5

(2) (you left out some important words)
|x+3|=(2/5) |y+1|

Multiply by 5 then simplify as before

(3) y=x becomes x-y=0 in general form.

Then use perpendicular distance formula using that line and the point (x,y), equating it to 2.
Simplify the resulting absolute value as before to get the equation.

 

[yoloswag]

Thank you braintic!!!! Great answer, helped me!