Perpendicular distance (1 Viewer)

[davidgoes4wce]

This question came from the El Hosri text book



My question is with the perpendicular distance can you use pythagoras theorem for Points A (-1,1) and Point E(1,-4) in order to determine the distance between the 2 points instead of using the perpendicular distance formula?

 

[Crisium]

Your midpoint looks a bit dodgy - you should double check it

+ If they ask you to find the perpendicular distance then use the formula - It's what the markers are most likely examining

+ You would be assuming that it is a right angled triangle

 

[davidgoes4wce]

That is the actual solution but my solution doing the distance by two points formula I got:





Obviously, they are 2 different answers but I think the logic behind what I did wasn't wrong.

 

[davidgoes4wce]

One of the questions in part (i) was to determine the midpoint of CD and to label it E, the solution says E is (1,-4)

 

[kawaiipotato]

That is the actual solution but my solution doing the distance by two points formula I got:





Obviously, they are 2 different answers but I think the logic behind what I did wasn't wrong.

How are you sure that the distance AE is in fact the perpendicular distance from A to line BE?

Gradient of line AE = -5/2 (if I were to construct a line)
Gradient of BE = 5

since -5/2 * 5 =/= -1, that means line AE and line BE cannot be perpendicular. Hence, the distance A to E cannot be perpedicular distance to line BE.
Your answer of sqrt29 is also greater than the given solution, which indicates that it's not the perpendicular distance.

A way for you to use pythagoras theorem is to find equation BE (already done) which allows you to find the gradient of perpendicular line to BE. You can then find equation of perpendicular line to BE passing through A. Solve those two equations together to find point X (poi) and then use pythag for AX (which will be the perpendicular distance.)

 

[davidgoes4wce]

I get it now.

If they state the 'distance AE' its a different thing to 'perpendicular distance A to line BE'. I see that my line was not 90 degrees as well.

 

[Crisium]

I get it now.

If they state the 'distance AE' its a different thing to 'perpendicular distance A to line BE'. I see that my line was not 90 degrees as well.

Yes because the perpendicular distance will be the shortest distance from that point to the line

They often ask "Find the shortest distance from Point A to the line y = ... " and so you use the perpendicular distance formula