Question

A triangle has corners at `(1, 7 )`, `( 8, 3 )`, and `( 4 , 8 )`. If the triangle is dilated by `2 x` around `(2, 5)`, what will the new coordinates of its corners be?

Answer 1

`(0,9),(14,1)" and "(6,11)`

Explanation:

`"label the vertices of the triangle"`

`A(1,7),B(8,3)" and "C(4,8)`

`"and A', B', C' the images of A, B and C"`

`"let the centre of dilatation be "D(2,5)`

`rArrvec(DA')=color(red)(2)vec(DA)`

`rArrula'-uld=2(ula-uld)=2ula-2uld`

`rArrula'=2ula-uld`

`color(white)(rArrula')=2((1),(7))-((2),(5))=((0),(9))`

`"the coordinates of A' are the components of "ula'`

`rArrA'=(0,9)`

`"similarly "`

`vec(DB')=color(red)(2)vec(DB)`

`rArrulb'=2ulb-uld`

`color(white)(rArrulb')=2((8),(3))-((2),(5))=((14),(1))`

`rArrB'=(14,1)`

`"and "vec(DC')=color(red)(2)vec(DC)`

`rArrulc'=2ulc-uld`

`color(white)(rArrulc')=2((4),(8))-((2),(5))=((6),(11))`

`rArrC'=(6,11)`

`color(blue)"Result after dilatation"`

`(1,7)to(0,9),(8,3)to(14,1),(4,8)to(6,11)`