Question

Which rule yields the dilation of the figure STUV centered at the origin? A) (x, y) → (5x, 5y) B) (x, y) → (0.2x, 0.2y) C) (x, y) → (x + 5, y + 5) D) (x, y) → (x + 0.2, y + 0.2)

Answer 1

A)
`(x,y)\rightarrow (5x,5y)`

Explanation:

The figure STUV has its coordinates at points S(1,-2), T(2,-1), U(1,2), V(0,-1).

Image quadrilateral S'T'U'V' has its coordinates at points S'(5,-10), T'(10,-5), U'(5,10), V'(0,-5).

As you cna see,

• 
  `S(1,-2)\rightarrow S'(5\cdot 1,5\cdot (-2));`
• 
  `T(2,-1)\rightarrow T'(5\cdot 2,5\cdot (-1));`
• 
  `U(1,2)\rightarrow U'(5\cdot 1,5\cdot 2);`
• 
  `V(0,-1)\rightarrow V'(5\cdot 0,5\cdot (-1)).`

So, the rule is

`(x,y)\rightarrow (5x,5y)`