Question

1. follow the directions for each dilation.

a. the dilation centered at q with a scale factor of 3/2
b. the dilation centered at o with a scale factor 1/2.
/4
(2c1q4)

Explanation:

Step1: Recall dilation formula

For a dilation centered at a point $(x_0,y_0)$ with scale - factor $k$, the new coordinates $(x',y')$ of a point $(x,y)$ are given by $(x',y')=(x_0 + k(x - x_0),y_0 + k(y - y_0))$.

Step2: Assume grid - based coordinates

Let's assume $Q$ has coordinates $(x_Q,y_Q)$, $P$ has coordinates $(x_P,y_P)$, $R$ has coordinates $(x_R,y_R)$ and $S$ has coordinates $(x_S,y_S)$.

For part a (dilation centered at $Q$ with $k = \frac{3}{2}$):

For point $P$:
$x_{P}'=x_Q+\frac{3}{2}(x_P - x_Q)=\frac{3}{2}x_P-\frac{1}{2}x_Q$
$y_{P}'=y_Q+\frac{3}{2}(y_P - y_Q)=\frac{3}{2}y_P-\frac{1}{2}y_Q$
Similarly, find the new coordinates of $R$ and $S$ using the same formula.

For part b (dilation centered at $O$ with $k=\frac{1}{2}$):

Let $O$ have coordinates $(x_O,y_O)$. For point $P$:
$x_{P}''=x_O+\frac{1}{2}(x_P - x_O)=\frac{1}{2}x_P+\frac{1}{2}x_O$
$y_{P}''=y_O+\frac{1}{2}(y_P - y_O)=\frac{1}{2}y_P+\frac{1}{2}y_O$
Similarly, find the new coordinates of $Q$, $R$ and $S$ using the same formula.

To actually find the new coordinates, we would need to assign numerical coordinates to the points $O$, $Q$, $P$, $R$ and $S$ based on the grid. But the general method for dilation is as shown above.

Since we don't have the numerical coordinates of the points, we can't give the exact final - answer coordinates. But the process for finding the dilated points is described.

If we assume we are just asked to describe the process, the above steps are sufficient. If we had numerical coordinates (e.g., $Q=(2,3)$, $P=(4,5)$ etc.), we would substitute those values into the formulas to get the new coordinates.

Answer:

Step1: Recall dilation formula

For a dilation centered at a point $(x_0,y_0)$ with scale - factor $k$, the new coordinates $(x',y')$ of a point $(x,y)$ are given by $(x',y')=(x_0 + k(x - x_0),y_0 + k(y - y_0))$.

Step2: Assume grid - based coordinates

Let's assume $Q$ has coordinates $(x_Q,y_Q)$, $P$ has coordinates $(x_P,y_P)$, $R$ has coordinates $(x_R,y_R)$ and $S$ has coordinates $(x_S,y_S)$.

For part a (dilation centered at $Q$ with $k = \frac{3}{2}$):

For point $P$:
$x_{P}'=x_Q+\frac{3}{2}(x_P - x_Q)=\frac{3}{2}x_P-\frac{1}{2}x_Q$
$y_{P}'=y_Q+\frac{3}{2}(y_P - y_Q)=\frac{3}{2}y_P-\frac{1}{2}y_Q$
Similarly, find the new coordinates of $R$ and $S$ using the same formula.

For part b (dilation centered at $O$ with $k=\frac{1}{2}$):

Let $O$ have coordinates $(x_O,y_O)$. For point $P$:
$x_{P}''=x_O+\frac{1}{2}(x_P - x_O)=\frac{1}{2}x_P+\frac{1}{2}x_O$
$y_{P}''=y_O+\frac{1}{2}(y_P - y_O)=\frac{1}{2}y_P+\frac{1}{2}y_O$
Similarly, find the new coordinates of $Q$, $R$ and $S$ using the same formula.

To actually find the new coordinates, we would need to assign numerical coordinates to the points $O$, $Q$, $P$, $R$ and $S$ based on the grid. But the general method for dilation is as shown above.

Since we don't have the numerical coordinates of the points, we can't give the exact final - answer coordinates. But the process for finding the dilated points is described.

If we assume we are just asked to describe the process, the above steps are sufficient. If we had numerical coordinates (e.g., $Q=(2,3)$, $P=(4,5)$ etc.), we would substitute those values into the formulas to get the new coordinates.