Question

In the xy-plane, line t passes through the origin and is perpendicular to the line 4x + y = k, where k is a constant. If the two lines interest at the point (t, t+1), what is the values of t?
a) -4/3
b) -5/4
c) 3/4
d) 5/4
e) 4/3

Answer 1

@mathslover I need help :3 pwease

Answer 2

@vishweshshrimali5

Answer 3

mmm
so the equation of the perpendicular line would be
some thing like y = (1/4)x + (k+1) ?

Answer 4

.-. I'm still confused sorry

Answer 5

Its ok.

Lets start from the very beginning:

(1) Let equation of line be y = mx

(2) Since its perpendicular to other line,so,

m*(-4) = -1

=> m = 1/4

(3) So, eq. becomes y = x/4
=> x = 4y

(4) Put x = 4y in second eq.,
we get,
4(4y) + y = k
=> y = k/(17)

So, x = 4y = (4k)/(17)

Thus, point of intersection is \((\cfrac{4k}{17}, \cfrac{k}{17})\).

But, it should be of the form (t,t+1). So,

\(\cfrac{k}{17} - \cfrac{4k}{17} = 1\)
\(\implies \cfrac{-3k}{17} = 1\)
\(\implies k = \cfrac{-17}{3}\)

So, \[t = \cfrac{4k}{17}\]
\[\implies t = \cfrac{4}{17}*\cfrac{-17}{3}\]
\[\implies t = \cfrac{-4}{3}\]

Answer 6

Did you get this ?

Answer 7

it's a little confusing... but I got lost at the k/17 - 4k/17 part
why did you do that? :/

Answer 8

See the point of intersection was supposed to be (t,t+1) but we got (4k/17, k/17). So on comparing, we get,
t = 4k/17
t+1 = k/17

Now, (t+1) - t = 1
=> (k/17) - (4k/17) = 1

Answer 9

ooohhhhhh
I see....
right
I remember doing something like t + 1 = 1/4 t
-> 3t = -4
t = -4/3
but answer key says C

Answer 10

oh wait nvm

Answer 11

I got it xD
thanks for your help! <3

Answer 12

It was my pleasure friends.