Co-ordinate Geometry help

Hello,

I was revising a few questions in which I am slightly stumped on how to start. I will post them as I go along but lets start with this question:

A quadrilateral has vertices A(0,0) B (0,3) C (6,6) and D (12,6)
i) draw the quadrilateral (done)
ii) show by calculation that it is a trapezium (done)
iii)find the co-ordinates of E when EBCD is a parallelogram (how?)

Thanks

(edited 12 years ago)

Reply 1

Tomcrease

For EBDC to be a parallelogram the gradient and length of BE must be the same as CD. So you can see that the gradient of CD is 0 as the y coordinates of C and D are the same. You can also work out it's length, x2 - x1 = 12 - 6 = 6.

See if you can work it out from there :smile:

Spoiler

(edited 12 years ago)

Reply 2

ztibor

10

Original post by rae_

Hello,

I was revising a few questions in which I am slightly stumped on how to start. I will post them as I go along but lets start with this question:

A quadrilateral has vertices A(0,0) B (0,3) C (6,6) and D (12,6)
i) draw the quadrilateral (done)
ii) show by calculation that it is a trapezium (done)
iii)find the co-ordinates of E when EBCD is a parallogran (how?)

Thanks

\vec r_E=\vec r_D+\vec {CB}=\vec r_B+\vec{CD}

with coordinates

x_E=0+(12-6)

y_E=3+(6-6)

Reply 3

rae_

OP

2

Thanks guys, you've been really helpful. Much appeciated however I didn't really understand the second method.

Any who I have another question:
The points A,B and C have co-ordinates 2,1 b,3 and 5,5 where b>3 and angle ABC is 90 find the value of B

I get the fact it has something to do with perpendicular lines but I have no ideas on how to go about it.

Thanks

OP

OP

help me please :frown:

Reply 6

ghostwalker

17

Original post by rae_

Any who I have another question:
The points A,B and C have co-ordinates 2,1 b,3 and 5,5 where b>3 and angle ABC is 90 find the value of B

I get the fact it has something to do with perpendicular lines but I have no ideas on how to go about it.

Thanks

If angle ABC is a right angle, then AB is perpendicular to BC.

So, what's the gradient of AB (in terms of b) ?

Siimilarly BC.

And since the two are perpendicular, the product of their gradients is -1.

See what you can do with that.

Co-ordinate Geometry help

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