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Sephiroth Valentine

Member

Registered: 2005-11-19

Posts: 6

Can any one help me with a coordinate geometry problem

rstu is a quadrilateral where r = (-1,-5) and s =  (13,9)
q(3,-1) lies on the line rs.

(i) The coordinates of u are (-2k,3k)
where k∈R and k>0

The area of the triangle rqu is 28 square units. Find the value of k.

(II) The slope of ts is -3/11 and sr are parallel to tu. Find the coordinates of t.

Would anyone be able to tell me the steps to take to solve these questions or would be able to offer suggestions of how to solve them thanks. Much appreciated

Last edited by MathsIsFun (2005-11-19 17:23:52)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Can any one help me with a coordinate geometry problem

Hi Sephiroth Valentine;

For i)

Coordinate geometry allows for more algebraic thrashing then Euclidean geometry.
You know you have 3 points given to you.
They are,

(-1,-5) which we call x1 and y1
(13,9) which we call x2 and y2
(-2k, 3k) which we call x3 and y3

The square brackets represent the determinant of a matrix.

Now just plug in to the above formula.

k = 2

To do ii) we start with a drawing of what we know already. See below, we know the coordinates of s, q , r , u.

The line segment rqs has an equation of y = x - 4

The line segment st has an equation of y = -(3/11)x + 138 / 11

The line segment ut has an equation of y = x + 10

From this we can determine t. We solve ut and st simultaneously

y = -(3/11)x + 138 / 11

y = x + 10

We get x = 2 , y = 12. So the coordinates of t are ( 2 , 12 ).

And we are done!

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Can any one help me with a coordinate geometry problem

hi Sephiroth Valentine

Help to attempt this:

Firstly make a good diagram so you can see what you have.  (see picture below)

I've had to choose where to put 'u' and 't'.  It's VERY unlikely I've put them in the right places so don't take the diagram as an answer!

You can box in any triangle like I've shown.  Getting its area is then a matter of working out the area of the box and subtracting the areas of the shaded (yellow) triangles.  They're all right angled so it shouldn't be too bad to calculate them.  You'll have to use these ideas to make an equation for 'k' and then solve it.  I haven't tried so I don't know how easy that will be.

second part. 

Calculate the equations for the lines st  and the parallel line that goes through t and u. (dotted on my diagram).

Use simultaneous equations to find where they cross."

That should do it.

Please post again if you need more details and, finally, to let us know you've done it.

Bob

Last edited by Bob (2010-10-23 23:41:33)

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Children are not defined by school ...........The Fonz
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Sometimes I deliberately make mistakes, just to test you!  …………….Bob