Question

A dilation maps (4, 6) to (2, 3). Under the same dilation, (-1,3) would be mapped to

Answer 1

`(-(1)/(2), (3)/(2))`.

Explanation:

Since, the rule of dilation about origin by the scale factor k is,

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

Given,

The dilation maps (4, 6) to (2, 3).

Let k be the scale factor for this dilation,

⇒ 4k = 2 ⇒ k =
`(2)/(4)=(1)/(2)`,

Thus, under the dilation rule would be,

`(x,y)\rightarrow ((1)/(2)x,(1)/(2)y)`

Hence, (-1,3) would be mapped to
`(-(1)/(2), (3)/(2))`.

Answer 2

(-1/2,3/2)

Explanation:

The rule for dilation about (0,0) by a scale factor is given as:

(x,y)----------(kx,ky)

So if (4,6) was mapped to (2,3) by dilation it means;

x=4

kx=2

k=2/4 =1/2

Hence in this case, the dilation rule is ;

(x,y)---------(1/2x ,1/2y)

For (-1,3) ---------(1/2*-1, 1/2*3)

(-1/2, 3/2)