A triangle has vertices at points A (2, 1), B (-2, 2) and C (3, 1).
After a dilation, the new vertices are at points A' (4, 2), B' (-4, 4) and C' (6, 2).
Determine the scale factor of the dilation.
To determine the scale factor of the dilation, we can calculate the distance between the original vertices and the corresponding new vertices.
Let's calculate the distance between A and A' using the distance formula:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
d = √[(4 - 2)^2 + (2 - 1)^2]
d = √[2^2 + 1^2]
d = √(4 + 1)
d = √5
Now, let's calculate the distance between B and B':
d = √[(-4 + 2)^2 + (4 - 2)^2]
d = √[(-6)^2 + 2^2]
d = √(36 + 4)
d = √40 = 2√10
Now, let's calculate the distance between C and C':
d = √[(6 - 3)^2 + (2 - 1)^2]
d = √[3^2 + 1^2]
d = √(9 + 1) = √10
The scale factor of the dilation can be calculated as the ratio of the corresponding distances between the original vertices and the new vertices.
Scale factor = Distance(A, A') / Distance(A, B') = √5 / 2√10 = 1 / 2
Therefore, the scale factor of the dilation is 1/2.
1) What was the result of the Boston Massacre?
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0 points
America gained independence.
The British surrendered.
Five colonists were killed.
The war reached a turning point.