Question

Find the image of P(7,7) under a dilation with scale factor 1/2 and center of dilation (1,3)

Answer 1

Given,

The coodinates of the points are P(7,7).

The scale factor is 1/2.

The coordinates of center of dilation is (1,3).

In the operation described here, it is the vector (center of dilation→ similar point) that will get multiplied by a factor 1/2.

The vector from the centre (1,3) to point (7,7) has coordinates (7,7) - (1,3)

`((7-1),(7-3))=(6,3)`

Now, dilated the coordinates by the scale factor of 1/2 then,

`(1)/(2)(6,3)=(3,(3)/(2))`

Image of the point is at,

`\begin{gathered} (3,(3)/(2))=(3+1,(3)/(2)+3) \\ =(4,(9)/(2)) \end{gathered}`

Hence, the coordinates of the image is (4,9/2).