Question

Hexagon FUTBOL has coordinates F(3,6), U(5,2), T(2,-3), B(-3,-2), O(-5,1) and L(-2,5), and it is dilated by scale factor of five centered at origin.

What are the coordinates of F'U'T'B'O'L'?

Answer 1

`F'(15,\ 30),\ U'(25,\ 10),\ T'(10,\ -15),\ B'(-15,\ -10),\ O'(-25,\ 5),\ L'(-10,\ 25)`

Explanation:

We known that ,

When a figure (with coordinate (x,y)) gets dilated by a scale factor k from origin (0,0) , then the coordinate of the new image will become :-

`(x,y)\to(kx,ky)`

Given : Hexagon FUTBOL has coordinates F(3,6), U(5,2), T(2,-3), B(-3,-2), O(-5,1) and L(-2,5), and it is dilated by scale factor of 5 centered at origin.

Then, the coordinates of F'U'T'B'O'L' will be :-

`F(3,6)\toF'(5(3),\ 5(6))=F'(15,\ 30)`

`U(5,2)\toU'(5(5),\ 5(2))=U'(25,\ 10)`

`T(2,-3)\toT'(5(2),\ 5(-3))=T'(10,\ -15)`

`B(-3,-2)\toB'(5(-3),\ 5(-2))=B'(-15,\ -10)`

`O(-5,1) \toO'(5(-5),\ 5(1))=O'(-25,\ 5)`

`L(-2,5) \toL'(5(-2),\ 5(5))=L'(-10,\ 25)`

Hence, the coordinates of F'U'T'B'O'L' will be :-

`F'(15,\ 30),\ U'(25,\ 10),\ T'(10,\ -15),\ B'(-15,\ -10),\ O'(-25,\ 5),\ L'(-10,\ 25)`