Question
line segment ab has endpoints a (-6, 4) and b (-8, 2). find the coordinates of a' and b' after a dilation with a scale factor of 1/2' centered at the origin.
a' (_,_)
b' (_,_)
a' (_,_)
b' (_,_)
Answers
Answered by
GPT 3.5
To find the coordinates of A' and B' after a dilation with a scale factor of 1/2 centered at the origin, we can use the formula for dilation:
A' = (1/2) * (A-O) + O
B' = (1/2) * (B-O) + O
Where A and B are the original coordinates, O is the center of dilation (in this case, the origin), and A' and B' are the new coordinates after the dilation.
For point A:
A' = (1/2) * (A - O) + O
= (1/2) * ((-6, 4) - (0,0)) + (0,0)
= (1/2) * (-6, 4) + (0,0)
= (-3, 2) + (0,0)
= (-3, 2)
So, the coordinates of A' are (-3, 2).
For point B:
B' = (1/2) * (B - O) + O
= (1/2) * ((-8, 2) - (0,0)) + (0,0)
= (1/2) * (-8, 2) + (0,0)
= (-4, 1) + (0,0)
= (-4, 1)
So, the coordinates of B' are (-4, 1).
Therefore, the coordinates of A' are (-3, 2) and the coordinates of B' are (-4, 1).
A' = (1/2) * (A-O) + O
B' = (1/2) * (B-O) + O
Where A and B are the original coordinates, O is the center of dilation (in this case, the origin), and A' and B' are the new coordinates after the dilation.
For point A:
A' = (1/2) * (A - O) + O
= (1/2) * ((-6, 4) - (0,0)) + (0,0)
= (1/2) * (-6, 4) + (0,0)
= (-3, 2) + (0,0)
= (-3, 2)
So, the coordinates of A' are (-3, 2).
For point B:
B' = (1/2) * (B - O) + O
= (1/2) * ((-8, 2) - (0,0)) + (0,0)
= (1/2) * (-8, 2) + (0,0)
= (-4, 1) + (0,0)
= (-4, 1)
So, the coordinates of B' are (-4, 1).
Therefore, the coordinates of A' are (-3, 2) and the coordinates of B' are (-4, 1).
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