Linear Crap!! Need help!!!

[squance]

My sister has homework and she's stuck on these! Can someone help? Thanks!

1. Find the angle the line joining the points make with the x-axis.
 (a). (-4,-3), (6,8)

2. Given that the line 4x-3y=10 and 4x-ay=m are perpendicular and intersect at the pint (4,2) find the values of x and a. (thorough solution please!)

3.Show that the point P(2,12) is equidistance from teh points A(3,5) and B(9,13). (Note: Equidistance means in teh middle of the 2 given points).

4.There is an off-shore drilling platform in Bass Strait situateda D (0,6) where 1 unit=5km. Pipes for this oil drill come ashore at M(-6,1) and N(3,-1). Assuming the pipelines are straight, which is the shortest, DM or DN? And what is its length? (to 1 dec. place)

[dcc]

1. a.

First step is to find the gradient of this graph:







Now think about this line, you can make lots and lots
of right angled triangles out of this line, but we are interested in the angle with the x-axis.

So we know that

And we know that opposite the angle we want is the height of the triangle and
the adjacent component is the base of the triangle, which is equivalent
to the gradient of the graph!

so:

[droodles]

perpendicular means that the gradient has to be divided under -1

[Collin Li]

(perpendicular gradient)



Equation:

Intersection at (4,2):

[Collin Li]

Equidistance is actually when the point is on the perpendicular bisector of two points. The midpoint is the middle of 2 points, and the midpoint is .

To prove equidistance, you find the distance from point P to A, and the distance from point P to B, and show they are the same value. You use Pythagoras' theorem for this:





(i.e.: equidistant)

[dcc]

2.

















Now, we know they are perpendicular where m is the gradient





















So:

and

[dcc]

omg coblin you ass pirate!

[Collin Li]

There is an off-shore drilling platform in Bass Strait situateda D (0,6) where 1 unit=5km. Pipes for this oil drill come ashore at M(-6,1) and N(3,-1). Assuming the pipelines are straight, which is the shortest, DM or DN? And what is its length? (to 1 dec. place)

Here you use Pythagoras' theorem again:





DN is shorter, and has a length of:

[Collin Li]

omg coblin you ass pirate!

You took too long

[dcc]

i did the last question but you beat me to that one too

i give up

[squance]

Thankyou once again guys!!!