Question

question 10 dilate line f by a scale factor of 3 with the center of dilation at the origin to create line f. where are points a and b located after dilation, and how are lines f and f related? the locations of a and b are a(0, 2) and b(6, 0); lines f and f intersect at point a. the locations of a and b are a(0, 6) and b(2, 0); lines f and f intersect at point b. the locations of a and b are a(0, 2) and b(2, 0); lines f and f are the same line. the locations of a and b are a(0, 6) and b(6, 0); lines f and f are parallel.

Explanation:

Step1: Recall dilation formula

If we have a point $(x,y)$ and a dilation with a scale - factor $k$ centered at the origin $(0,0)$, the new point $(x',y')$ is given by $(x',y')=(kx,ky)$.

Step2: Assume coordinates of A and B

Let's assume point $A=(0,2)$ and point $B=(2,0)$ (since no coordinates are given in the problem statement, we can work with general - looking points on a line for illustration). If the scale factor $k = 3$, for point $A=(0,2)$, $A'=(3\times0,3\times2)=(0,6)$; for point $B=(2,0)$, $B'=(3\times2,3\times0)=(6,0)$.

Step3: Analyze the relationship between the lines

When a line is dilated with the center of dilation at the origin, the original line and the dilated line are parallel.

Answer:

The locations of $A'$ and $B'$ are $A'(0,6)$ and $B'(6,0)$; lines $f$ and $f'$ are parallel.