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 the dilation at the origin (0,0)

Answer 1

The dilation with a scale factor of 2 and a center point of the origin (0,0) will stretch the line segments AB and CD away from the origin.

For line segment AB, the dilation will result in a new line segment A'B', where the coordinates of A' and B' are twice the x-coordinates and the y-coordinates of A and B, respectively.

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

So, the new line segment A'B' can be described as A'(-14, 4) and B'(-8, 10).

For line segment CD, the coordinates of C' and D' will also be twice the x-coordinates and the y-coordinates of C and D, respectively.

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

So, the new line segment C'D' can be described as C'(-12, -2) and D'(-6, 4).

Overall, the effect of the dilation with a scale factor of 2 and a center point of the origin (0,0) will stretch the line segments AB and CD away from the origin, resulting in the new line segments A'B' and C'D'.