# Stuck on questions! :(

• Jun 10th 2007, 09:15 AM
Danielisew
Stuck on questions! :(
Ok i got a grid here with x going from -5 to +5 and y going from -5 to +5.
I need to enlarge Triangle A by scale factor -1/2, centre (-1,-2).

The coordinates of the Triangle A are:

(1,-4) (3,-4) (1,2)

Please can someone roughly draw out this enlargement i am stuck!
• Jun 10th 2007, 09:36 AM
earboth
Quote:

Originally Posted by Danielisew
Ok i got a grid here with x going from -5 to +5 and y going from -5 to +5.
I need to enlarge Triangle A by scale factor -1/2, centre (-1,-2).

The coordinates of the Triangle A are:
(1,-4) (3,-4) (1,2)
Please can someone roughly draw out this enlargement i am stuck!

Hello,

I've attached the sketch:
• Jun 10th 2007, 09:45 AM
Danielisew
Thanks, but how exactly did you do it?

Did you measure the distance between the centre point, and the corners of the original triangle, and then half these to make the new one, or what? :D

Thanks
• Jun 10th 2007, 10:27 AM
Danielisew

I got a real GCSE exam tomorrow and need an A!
At this rate, this impossible paper is putting me down and ill probs get a D!!!!
• Jun 10th 2007, 11:40 AM
earboth
Quote:

Originally Posted by Danielisew
Thanks, but how exactly did you do it?

Did you measure the distance between the centre point, and the corners of the original triangle, and then half these to make the new one, or what? :D

Thanks

Hello,

it's me again:

You are dealing with a "central projection" (this word is literally translated from German). That means you have an original (point, figure) and a description how to construct the image of this original using a centre of projection. This centre C is the only fixed point of the projection:

Let P be the original point
let P' be the image of P
let C be the centre of the projection:

Then the central projection is done by:

1. PP'C lie on a straight line.
2. The ratio $\frac{P'C}{PC}= k$ is a constant.

If 0 < k < 1 then P' lies between C and P
If k > 1 then P lies between C and P'
If k < 0 then C lies between P and P'

How I did the drawing:

1. draw the triangle
2. draw the centre C
3. connect each vertex of the triangle with C
4. lengthen the straight line PC by the half of PC
5. the end of this lengthened straight line is P'
6. Connect all points P': You got the image of the triangle
• Jun 10th 2007, 12:30 PM
Danielisew
thanks a lot