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' (_,_)

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).
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