Final Answer:
The scale factor that was used in the dilation is 2/3, So the correct option is b.
Step-by-step explanation:
To determine the scale factor used in the dilation of the given triangle, we will need to compare the coordinates of the original points with their corresponding dilated points.
The formula to find the scale factor is as follows:
If you have an original point (x1, y1) and a dilated point (x2, y2), then the scale factor `k` is found by dividing the coordinates of the dilated point by the corresponding coordinates of the original point. This means the scale factor k based on x-coordinates is k = (x2/x1), and the scale factor k based on y-coordinates is k = (y2/y1).
We will apply this formula to find the scale factor for each vertex of the triangle, and it should be the same for all vertices if the dilation was uniform.
For J:
Original coordinates: (-3, -12)
Dilated coordinates: (-2, -8)
To find the scale factor based on x-coordinates: kx = (-2) / (-3) = 2/3
To find the scale factor based on y-coordinates: ky = (-8) / (-12) = 8/12 = 2/3
For K:
Original coordinates: (-6, -15)
Dilated coordinates: (-4, -10)
To find the scale factor based on x-coordinates: kx = (-4) / (-6) = 4/6 = 2/3
To find the scale factor based on y-coordinates: ky = (-10) / (-15) = 10/15 = 2/3
For L:
Original coordinates: (-9, -12)
Dilated coordinates: (-6, -8)
To find the scale factor based on x-coordinates: kx = (-6) / (-9) = 6/9 = 2/3
To find the scale factor based on y-coordinates: ky = (-8) / (-12) = 8/12 = 2/3
For the dilation to be consistent, the scale factors calculated from all x-coordinates (kx) and all y-coordinates (ky) should be the same.
From our calculations, we've found that the scale factor for all points is 2/3 based on both the x-coordinates and the y-coordinates.
Therefore, the scale factor that was used in the dilation of the triangle is 2/3, So the correct option is b.
Complete question:
The coordinates below represent a triangle that was dilated.
J(-3, -12) → J'(-2,-8)
K(-6, -15) → K'(-4,-10)
L(-9, -12) → L'(-6,-8)
What was the scale factor that was used in the dilation?
a) 1/2
b) 2/3
c) 3/2
d) 1/3