Line AB and line CD are parallel lines. Line AB contains the points A(−7,2) and B(−4,5), and line CD contains the points C(−6,−1) and D(−3,2). Describe the effect of the dilation with a scale factor of 2 and a center point of dilation at the origin (0,0).(1 point)
1.After dilation, the lines are two units closer to the point of dilation. The resulting points are A′ (−14,4), B′ (−8,10), C′(−12,−2), and D′(−6,4).
2.After dilation, the lines are two units closer to the point of dilation. The resulting points are A′ (−72,1), B′(−2,52), C′(−3,−12), and D′(−32,1).
3.After dilation, the lines are two units farther from the point of dilation. The resulting points are A′ (−5,4), B′ (−2,7), C′(−4,1), and D′(−1,4).
4.After dilation, the lines are two units farther from the point of dilation. The resulting points are A′ (−14,4), B′ (−8,10), C′(−12,−2), and D′(−6,4).
The correct answer is 1. After dilation, the lines are two units closer to the point of dilation. The resulting points are A′ (−14,4), B′ (−8,10), C′(−12,−2), and D′(−6,4).
To understand the effect of a dilation with a scale factor of 2 and a center point of dilation at the origin (0,0), we need to multiply the coordinates of each point by the scale factor.
The given points are:
A(-7,2)
B(-4,5)
C(-6,-1)
D(-3,2)
To find the new coordinates after dilation, we multiply each coordinate by 2.
For point A:
A' = (-7*2, 2*2) = (-14, 4)
For point B:
B' = (-4*2, 5*2) = (-8, 10)
For point C:
C' = (-6*2, -1*2) = (-12, -2)
For point D:
D' = (-3*2, 2*2) = (-6, 4)
Therefore, the resulting points after dilation are:
A'(-14, 4)
B'(-8, 10)
C'(-12, -2)
D'(-6, 4)
So, the correct answer is option 1.
After dilation, the lines are two units closer to the point of dilation. The resulting points are A'(-14, 4), B'(-8, 10), C'(-12, -2), and D'(-6, 4).