Question

what is the scale factor used to dilate the triangle shown below.

Explanation:

Step1: Determine length of AB

From the graph, let's assume each grid is 1 unit. The coordinates of A and B: Let's say A is at (2,1) and B is at (6,1) (approximate from the grid). So length AB = 6 - 2 = 4 units.

Step2: Determine length of A'B'

Coordinates of A' and B': A' is at (8,2) and B' is at (20,2) (approximate). Length A'B' = 20 - 8 = 12 units.

Step3: Calculate scale factor

Scale factor = $\frac{\text{Length of image (A'B')}}{\text{Length of original (AB)}}$ = $\frac{12}{4}$ = 3.
Alternatively, we can check the height. Original height (from C to AB): C is at (4,6), AB is at y=1, so height is 6 - 1 = 5? Wait, maybe better to take the base. Wait, maybe my initial coordinates were wrong. Let's re - check. Looking at the small triangle: A is at (2,1), B is at (6,1), so AB length is 4 (from x=2 to x=6). The big triangle: A' is at (8,2), B' is at (20,2), so A'B' length is 12 (20 - 8). So scale factor is 12/4 = 3. Also, the height of small triangle: C is at (4,6), so height is 6 - 1 = 5? Wait, no, the small triangle's height: from y=1 to y=6, so 5 units? Wait, the big triangle's C' is at (16,18), and A'B' is at y=2, so height is 18 - 2 = 16? Wait, that doesn't match. Wait, maybe I messed up the y - coordinates. Let's take the base again. The small triangle's base AB: let's count the number of grids. From A to B, how many horizontal grids? Let's see, A is at (2,1), B is at (6,1), so 4 grids. The big triangle's base A'B': from A' (8,2) to B' (20,2), that's 12 grids. So 12/4 = 3. So scale factor is 3.

Answer:

3