Question

look at triangle abc.
what are the coordinates of the image of point b after a dilation with center and scale factor 3?
a $(-3, 3)$
c $(2, 1)$
b $(-1, 4)$
d $(\frac{1}{3}, \frac{1}{3})$

Explanation:

Step1: Identify coordinates of B

From the graph, point B has coordinates \((-1, 1)\) (wait, no, looking at the graph, B is at \((-1, 1)\)? Wait, no, the grid: x-axis, y-axis. Let me check again. Wait, the center of dilation is the origin? Wait, the problem says "dilation with center" – maybe center at origin? Wait, the original point B: looking at the graph, B is at \((-1, 1)\)? Wait, no, the blue triangle: C is at \((-3, 0)\), B is at \((-1, 1)\), A is at \((-2, 3)\). Wait, the problem says "dilation with center" – maybe center at origin? Wait, the options: let's re-express. Wait, maybe the center is the origin? Wait, no, maybe the center is point C? Wait, no, the problem says "dilation with center" – maybe a typo, maybe center at origin. Wait, no, let's check the options. Wait, the original coordinates of B: from the graph, B is at \((-1, 1)\)? Wait, no, looking at the x and y axes: x=-1, y=1? Wait, the grid lines: x from -5 to 5, y from -4 to 4. So B is at (-1, 1). Wait, but the options: A is (-3,3), B is (-1,4), C is (2,1), D is (1/3,1/3). Wait, maybe the center of dilation is the origin, and scale factor 3? Wait, no, dilation with scale factor 3: if center is origin, then (x,y) becomes (3x, 3y). But B is at (-1,1), so 3(-1)=-3, 31=3, so (-3,3), which is option A. Wait, that makes sense. So step 1: find coordinates of B. From the graph, B is at (-1, 1). Step 2: apply dilation with center at origin (assuming, since it's a common case) and scale factor 3. So the formula for dilation with center (0,0) and scale factor k is \((x,y) \to (kx, ky)\). So x-coordinate: -1 3 = -3, y-coordinate: 1 3 = 3. So the image is (-3, 3), which is option A.

Answer:

A. (-3, 3)