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)
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'.
To describe the effect of the dilation with a scale factor of 2 and a center point at the origin (0,0) on lines AB and CD, we need to find the new coordinates of the points A, B, C, and D after the dilation.
For a dilation with a scale factor of 2, the new coordinates can be found by multiplying the original coordinates by the scale factor.
Let's calculate the new coordinates for each point:
Point A: (-7, 2)
The new coordinates for point A after the dilation will be:
New coordinates for A = 2 * (-7, 2)
= (-14, 4)
Point B: (-4, 5)
The new coordinates for point B after the dilation will be:
New coordinates for B = 2 * (-4, 5)
= (-8, 10)
Point C: (-6, -1)
The new coordinates for point C after the dilation will be:
New coordinates for C = 2 * (-6, -1)
= (-12, -2)
Point D: (-3, 2)
The new coordinates for point D after the dilation will be:
New coordinates for D = 2 * (-3, 2)
= (-6, 4)
Therefore, after the dilation with a scale factor of 2 and a center point at the origin (0,0), the new coordinates of the points on line AB are (-14, 4) and (-8, 10), and the new coordinates of the points on line CD are (-12, -2) and (-6, 4).