A triangle has corners at #(1, 7 )#, #( 8, 3 )#, and #( 4 , 8 )#. If the triangle is dilated by # 2 x# around #(2, 5)#, what will the new coordinates of its corners be?
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To dilate the triangle by a factor of 2 around the point (2, 5), we'll use the dilation formula for coordinates (x', y'):
[ x' = k(x - h) + h ] [ y' = k(y - v) + v ]
Where:
- (x, y) are the original coordinates of a point in the triangle,
- (h, v) are the coordinates of the center of dilation (in this case, (2, 5)),
- k is the scale factor of dilation (2 in this case),
- (x', y') are the new coordinates after dilation.
Let's calculate the new coordinates for each corner of the triangle:
-
For the point (1, 7): [ x' = 2(1 - 2) + 2 = 0 + 2 = 2 ] [ y' = 2(7 - 5) + 5 = 2 + 5 = 7 ] So, the new coordinates are (2, 7).
-
For the point (8, 3): [ x' = 2(8 - 2) + 2 = 12 ] [ y' = 2(3 - 5) + 5 = 1 ] So, the new coordinates are (12, 1).
-
For the point (4, 8): [ x' = 2(4 - 2) + 2 = 6 ] [ y' = 2(8 - 5) + 5 = 11 ] So, the new coordinates are (6, 11).
Therefore, after dilation by a factor of 2 around (2, 5), the new coordinates of the triangle's corners will be (2, 7), (12, 1), and (6, 11).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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