Question

1. is located at (6, -10). a dilation centered at the origin with scale factor of (k=\frac{3}{2}) is performed on (j) to form (j). is this an example of a reduction or an enlargement? what are the coordinates of (j)?

Explanation:

Step1: Determine reduction or enlargement

Since the scale factor $k=\frac{3}{2}=1.5> 1$, it is an enlargement.

Step2: Find new coordinates

If a point $(x,y)$ is dilated with a scale - factor $k$ centered at the origin, the new coordinates $(x',y')$ are given by $(x',y')=(kx,ky)$. Here $x = 6$ and $y=-10$, $k=\frac{3}{2}$. So $x'=\frac{3}{2}\times6 = 9$ and $y'=\frac{3}{2}\times(-10)=-15$.

Answer:

It is an enlargement. The coordinates of $J'$ are $(9, - 15)$.