Question

1. (03.01 lc)

\overline{ab} is dilated from the origin to create \overline{ab} at a (0, 4) and b (4, 6). what scale factor was \overline{ab} dilated by? (1 point)
\bigcirc \\ \frac{1}{2}
\bigcirc \\ 2
\bigcirc \\ 3
\bigcirc \\ 4

1. the goal of spiritual growth is to \underline{qquad}.

\bigcirc \\ become more like christ
\bigcirc \\ get more noticed at church

Explanation:

Step1: Find coordinates of A and B

From the graph, \(A=(0,2)\) and \(B=(2,3)\)

Step2: Use dilation formula

If a point \((x,y)\) is dilated from the origin \((0,0)\) by a scale factor \(k\) to \((x',y')\), then \(x' = kx\) and \(y'=ky\).
For point \(A\): \(A=(0,2)\) and \(A'=(0,4)\). Using \(y' = ky\), we have \(4=k\times2\), so \(k = 2\).
We can also check for point \(B\): \(B=(2,3)\), if \(k = 2\), then \(x'=2\times2 = 4\) and \(y'=2\times3=6\) which matches \(B'=(4,6)\)

Answer:

2