Question

plot the image of point a under a dilation about point p with a scale factor of 3.

Explanation:

Step1: Determine vector from P to A

Let the coordinates of point $P$ be $(x_p,y_p)$ and of point $A$ be $(x_a,y_a)$. The vector $\overrightarrow{PA}=(x_a - x_p,y_a - y_p)$.

Step2: Multiply vector by scale - factor

The new vector for the dilated point $A'$ with a scale - factor of $3$ is $\overrightarrow{PA'}=3\overrightarrow{PA}=(3(x_a - x_p),3(y_a - y_p))$.

Step3: Find coordinates of dilated point

The coordinates of the dilated point $A'$ are $(x_a',y_a')=(x_p+3(x_a - x_p),y_p + 3(y_a - y_p))=(3x_a-2x_p,3y_a - 2y_p)$. On the grid, count the horizontal and vertical distances from $P$ to $A$, then multiply those distances by $3$ and go from $P$ in the same direction to plot $A'$.

Answer:

To plot the point accurately on the grid, count the number of grid - squares horizontally and vertically from $P$ to $A$. Multiply those counts by $3$ and starting from $P$, move in the same horizontal and vertical directions to mark the new point (the image of $A$ under the dilation). Without specific coordinates for $P$ and $A$, we can't give exact numerical coordinates for the new point, but this is the method for plotting.