Line AB
and line CD
are parallel lines. Line AB
contains the points A(−5,−5)
and B(−3,−2)
, and line CD
contains the points C(−7,−2,)
and D(−5,1)
. Describe the effect of the dilation with a scale factor of 3 and a center point of dilation at the origin (0,0)
.
Option #1: After dilation, the lines are three units farther from the point of dilation. The resulting points are A′ (−2,−2)
, B′ (0,1)
, C′(−4,1)
, and D′(−2,4)
. The dilated lines are parallel.
Option #2: After dilation, the lines are three units closer to the point of dilation. The resulting points are A′ (−53,−53)
, B′(−1,−23)
, C′(−72,−23)
, and D′(−53,13)
. The dilated lines are parallel.
Option #3: After dilation, the lines are three units farther from the point of dilation. The resulting points are A′(−15,−15)
, B′(−9,−6)
, C′(−21,−6)
, and D′(−15,3)
. The dilated lines are parallel
Option #1: After dilation, the lines are three units farther from the origin. The resulting points are A'(-15, -15), B'(-9, -6), C'(-21, -6), and D'(-15, 3). The dilated lines are parallel.
Therefore, Option #1 is the correct description of the effect of the dilation with a scale factor of 3 and a center point of dilation at the origin.
Mine says 3 is correct
I apologize for the error. Yes, Option #3 accurately describes the effect of the dilation with a scale factor of 3 and a center point of dilation at the origin. The resulting points are A'(-15, -15), B'(-9, -6), C'(-21, -6), and D'(-15, 3), and the dilated lines remain parallel. Thank you for pointing that out.
But how
To determine the effect of the dilation with a scale factor of 3 and a center point at the origin (0,0), we need to apply the formula for dilation.
The formula for dilation is:
P'(x', y') = k * (P - O) + O
Where:
- P(x, y) is the original point
- O(0, 0) is the center of dilation
- P'(x', y') is the new point after dilation
- k is the scale factor
Let's calculate the new points A', B', C', and D':
For point A(-5, -5):
A'(-15, -15) = 3 * (-5, -5) + (0, 0)
A'(-15, -15) = (-15, -15)
For point B(-3, -2):
B'(-9, -6) = 3 * (-3, -2) + (0, 0)
B'(-9, -6) = (-9, -6)
For point C(-7, -2):
C'(-21, -6) = 3 * (-7, -2) + (0, 0)
C'(-21, -6) = (-21, -6)
For point D(-5, 1):
D'(-15, 3) = 3 * (-5, 1) + (0, 0)
D'(-15, 3) = (-15, 3)
Therefore, the new points after dilation with a scale factor of 3 and a center point at the origin are A'(-15, -15), B'(-9, -6), C'(-21, -6), and D'(-15, 3). The lines AB and CD remain parallel after dilation.