Finding the Value of K with Points, Determing Angle of Eleva

[Teksunai]

Hello again! It's me Teksunai hen.

I've some more problems.

I need help to solve'em.

The first one is

Find the equation of the line through the origin which is perpendicular to the line 2x+3y-4=0

Okay, a few things I am confused about.

First off, what is this origin spoken about? I do not know how to find the origin to this, what I do know is that I should convert this to slope-intercept form, and mayhaps find the y-intercept.

So

3y=-2x+4

Divide everything by 3 to be rid of 3y.

y=(-2/3)x+(4/3)

m= (-2/3) perpendicular is the opposite sign reciprocal so m=(3/2)

Or is this even necessary? Should I be able to use the slope -2 and convert it to the perpendicular? Would it be fraction(1/2) instead? What determines when you can simply use the slope in the question, or have to go through other steps to find the slope?

Then we find the y-intercept using the y-intercept method

So y=

3y=-2x+4
3y=-2(0)+4
3y=4

Divide by three to be rid of 3y

y=(4/3)
Which should be right.

So the answer should be

y=(1/2)x+(4/3).

However, this is COMPLETELY WRONG!

The answer is
3x-2y=0


I understand part of the reason why this is wrong now; I point it into slope-intercept form when it was not asked, however, I have no idea how to do this question! Word problems are definately not a gift of mine and I need to be able to locate the keywords in this word problem to associate it with what I must do, which I honestly need help with. I am not even 100% what it is asking for. Step by step followed by logic would be nice if possible please... Dx

Second question!

The point (3,k) is exactly 5 units away from (0,0). What is the value of k?

'Kay, what I have trouble with is figuring out what five represents exactly.

Is it the slope? Some random y-intercept? I'd imagine the slope because it is represented by one 'coordinate' as to call it, so to solve for k, it should be a simple m=rise/run equation.

So it should be
m=(y2-y1)
______
(x2-x1)

5=k-0
___
3-0

5=(k/3)Fraction

Multiply denominator 3 on both sides to be ride of it.

15=k.

This sounds reasonable and logical to me, it's what sticks out to me.

WRONG!

ANSWER IS k=4 or k=-4
How do you get that? D:

Third question!

An observer stands 40 meters from a high cliff. The angle of elevation to the top of the cliff is 53 degrees. How high is the cliff?

Okay, the only thing that came to mind was SOH CAH TOA, however, we don't even know if this has a 90 degree angle, logically! You'd think the ground would be perpendicular where the cliff first starts, but that depends how steep the cliff is. I do not know how to solve this.

If there is any website or any forming or any teaching site I can go to that will help me with word problems or teach me what I need to do or help ram these lessons in my head properly, please tell me! I hate relying on people when I do my best to figure it out myself, but I cannot; what I have trouble with right now is knowing exactly what a question is asking or by what method by it's wording and other areas that I cannot specify at current moment. I do not like the fact less than 20 questions takes me 2 hours to do and I need to know how to do all of this; I appreciate the help you have been giving me, and I do not wish to exploit it any further.

Anyway, that's all for today.

I love you guys and thank you so much for you help!

-Teksunai

 

[Mrspi]

Hello again! It's me Teksunai hen.

I've some more problems.

I need help to solve'em.

The first one is

Find the equation of the line through the origin which is perpendicular to the line 2x+3y-4=0

Okay, a few things I am confused about.

First off, what is this origin spoken about? I do not know how to find the origin to this, what I do know is that I should convert this to slope-intercept form, and mayhaps find the y-intercept.

So

3y=-2x+4

Divide everything by 3 to be rid of 3y.

y=(-2/3)x+(4/3)

m= (-2/3) perpendicular is the opposite sign reciprocal so m=(3/2)

Or is this even necessary? Should I be able to use the slope -2 and convert it to the perpendicular? Would it be fraction(1/2) instead? What determines when you can simply use the slope in the question, or have to go through other steps to find the slope?

Then we find the y-intercept using the y-intercept method

So y=

3y=-2x+4
3y=-2(0)+4
3y=4

Divide by three to be rid of 3y

y=(4/3)
Which should be right.

So the answer should be

y=(1/2)x+(4/3).

However, this is COMPLETELY WRONG!

The answer is
3x-2y=0


I understand part of the reason why this is wrong now; I point it into slope-intercept form when it was not asked, however, I have no idea how to do this question! Word problems are definately not a gift of mine and I need to be able to locate the keywords in this word problem to associate it with what I must do, which I honestly need help with. I am not even 100% what it is asking for. Step by step followed by logic would be nice if possible please... Dx

i

The "origin" is the point (0, 0) where the x-axis and the y-axis intersect.

So, you are looking for the equation of a line through (0, 0) that is perpendicular to the given line, 2x + 3y - 4 = 0.

You've already solved this equation for y:

y = (-2/3)x + (4/3)

You've already determined that the slope of a perpendicular to this line would have a slope of 3/2....

Now...use the point-slope form for the equation of a line:

y - y1 = m(x - x1)

m = 3/2
(x1, y1) = (0, 0)

y - 0 = (3/2)(x - 0)
y = (3/2)x

 

[Denis]

The point (3,k) is exactly 5 units away from (0,0). What is the value of k?

Get some graph paper and plot an "approximate" (3,k); make k = 4.
So this means that a straight line from the origin (0,0) to point(3,4) is 5 units in length.
Now draw a perpendicular line from point(3,4) to x-axis: see a nice easy-to-handle right triangle?
Getting back to k, can you see that k^2 + 3^2 = 5^2 ?
Yes, it's that simple.
The 2nd answer is due to fact that k can also lie below the x-axis. Kapish?