Question

question 12
a rectangle has a length of 6 units and a width of 4 units. after a dilation centered at the origin with a scale factor of (1)/(2), what will be the new length and width?
3 units by 2 units
6 units by 2 units
12 units by 8 units
4 units by 2 units
a triangle has its vertices at (0,0), (2,0), and (0,3). if the triangle is dilated by a scale factor of 2 centered at the origin, what are the coordinates of the image of the point (2,0)?
(0,2)
(1,0)
(2,0)
(4,0)

Explanation:

Step1: Recall dilation formula for length

For a dilation with scale - factor $k$ centered at the origin, if the original length is $l$, the new length $l'=k\times l$.

Step2: Identify values of $k$ and $l$

The original length $l = 6$ units and the scale - factor $k=\frac{1}{2}$.

Step3: Calculate new length

$l'=\frac{1}{2}\times6 = 3$ units.

Answer:

3 units by 2 units