Question

What if it was dilated about the point (1,1)?

Answer 1

H=(-8,14)

G=(-3,6)

Explanation:

The meaning of dilation is : The distance between the numbers or consecutives values increases by a factor which is known as the dilation factor. Now if the graph is dilated about origin , it means the origin is in the same position as before but the rest move .

Given :

• The initial co-ordinates of H is (-4,7)
• The initial co-ordinates of G is (-1,3)

If the graph is dilated about (1,1) , (1,1) is fixed.

Thus , the distance in the x-axis from the point (1,1) increases.

distance of x-coordinate of H from (1,1) = (1-(-4))=5;

Thus , it increases
`5*2 = 10` times.

but since it's measured from 1 ,

it's x coordinate becomes : -10+2=-8

Similarly , the y coordinate :

distance = 7-1 = 6 ;

increases to = 12 ;

measured from 1 , thus it's original value will be 12+2=14;

new coordinates of H is ( -8,14)

G:

distance from x :

-1-1=2;

increment :
`2*2=4`

coordinate : -1-4+2 = -3

distance from y : 3-1=2

increment :
`2*2=4`

total increment : 4+2 =6

new coordinates : ( -3,6)