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, $\overrightarrow{PA'}=3\overrightarrow{PA}=(3(x_a - x_p),3(y_a - y_p))$.

Step3: Find coordinates of dilated point $A'$

If we let the coordinates of $A'$ be $(x_{a'},y_{a'})$, then $x_{a'}=x_p+3(x_a - x_p)=3x_a - 2x_p$ and $y_{a'}=y_p+3(y_a - y_p)=3y_a - 2y_p$. On the grid, count the horizontal and vertical distances from $P$ to $A$, multiply those distances by 3, and then plot the new point $A'$ relative to $P$.

Answer:

Plot the new point $A'$ according to the calculated distances from $P$ on the grid. (Since no grid - based coordinates are given for $P$ and $A$, the general method of finding the dilated point is presented).