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) .

Answer 1

The dilation with a scale factor of 2 and a center point of dilation at the origin would stretch or shrink the line segments connected by A and B and C and D. In this case, since the scale factor is 2, the line segments would be stretched by a factor of 2.

To find the new coordinates of the points A and B after the dilation, we multiply each coordinate by 2:

A' = (-7*2, 2*2) = (-14, 4)
B' = (-4*2, 5*2) = (-8, 10)

Similarly, for the points C and D, we multiply each coordinate by 2:

C' = (-6*2, -1*2) = (-12, -2)
D' = (-3*2, 2*2) = (-6, 4)

The new line AB' would pass through the points A' (-14, 4) and B' (-8, 10), while the new line CD' would pass through the points C' (-12, -2) and D' (-6, 4). These new lines would be parallel to each other, just like the original lines AB and CD.