Question

plot the image of point a under a dilation about point p with a scale factor of 4.

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 $A'$ relative to $P$ is $\overrightarrow{PA'}=4\overrightarrow{PA}=(4(x_a - x_p),4(y_a - y_p))$.

Step3: Find coordinates of dilated point

The coordinates of the dilated point $A'$ are $(x_p+4(x_a - x_p),y_p + 4(y_a - y_p))=(4x_a-3x_p,4y_a - 3y_p)$. On the grid, count the horizontal and vertical distances from $P$ to $A$, multiply those distances by 4, and then plot the new point $A'$ starting from $P$.

Answer:

Plot the new point $A'$ according to the above - calculated coordinates or vector operations on the grid.