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Finding the equation of a reflected line [FP3]

OCR June 2010 paper, question 7iii:
Screen Shot 2013-06-07 at 14.01.53.png
Mark scheme:
Screen Shot 2013-06-07 at 14.02.03.png

Could somebody please explain 7iii to me please? I don't understand where the k=4 comes from in the mark scheme.
Thanks!
Reply 1
Avatar for imnotanewb
imnotanewb
AHA! i think i know (for once)

l1 (the original line), is 2 distant from the plane. (k=2)

As you are finding a reflection (in the plane) of the line, it follows that the line l2 (the new line) is also 2 distant from the plane, but on the other side of the plane from l1.

so you have (k=2) - (k=-2)
k= 2-(-2) =4.

i think. im probably failing FP3 anyway, so i could be wrong.
(edited 10 years ago)
Reply 2
Avatar for Supertod
Supertod
OP
Original post by imnotanewb
AHA! i think i know (for once)

l1 (the original line), is 2 distant from the plane. (k=2)

As you are finding a reflection (in the plane) of the line, it follows that the line l2 (the new line) is also 2 distant from the plane, but on the other side of the plane from l1.

so you have (k=2) - (k=-2)
k= 2-(-2) =4.

i think. im probably failing FP3 anyway, so i could be wrong.


I thought the distance was 2root21 though?
Original post by Supertod
OCR June 2010 paper, question 7iii:
Screen Shot 2013-06-07 at 14.01.53.png
Mark scheme:
Screen Shot 2013-06-07 at 14.02.03.png

Could somebody please explain 7iii to me please? I don't understand where the k=4 comes from in the mark scheme.
Thanks!

The whole purpose of choosing k=4 is to obtain a point on the new line. You know from the previous part that setting k=2 in the vector equation (for the line through (-7,-3,0) perp. to the plane) gives you a point on the plane. By symmetry, to reach a point on the reflected line, you need to go an identical distance further after reaching the plane. This corresponds to an extra "+2" on the value of k and hence choosing k=4 gives you a point on the new line. The line was parallel to the plane before you reflected it so the reflected line will also be parallel to the old line, giving you the direction vector too.
(edited 10 years ago)
Reply 4
Avatar for Supertod
Supertod
OP
Original post by Farhan.Hanif93
The whole purpose of choosing k=4 is to obtain a point on the new line. You know from the previous part that setting k=2 in the vector equation (for the line through (-7,-3,0) perp. to the plane) gives you a point on the plane. By symmetry, to reach a point on the reflected line, you need to go an identical distance further after reaching the plane. This corresponds to an extra "+2" on the value of k and hence choosing k=4 gives you a point on the new line. The line was parallel to the plane before you reflected it so the reflected line will also be parallel to the old line, giving you the direction vector too.


Ah right, I used a different method for part ii, so I didn't get a value for k. I understand now, thanks.

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