Question

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 a point $(x,y)$ dilated by a scale - factor $k$ centered at the origin, the new coordinates $(x',y')$ are given by $(x',y')=(k\cdot x,k\cdot y)$.

Step2: Identify the point and scale - factor

The point is $(2,0)$ and the scale - factor $k = 2$.

Step3: Calculate the new coordinates

$x'=2\times2 = 4$ and $y'=2\times0 = 0$. So the new coordinates are $(4,0)$.

Answer:

$(4,0)$