Select the coordinates A' and B' after dilation of the line segment AB with a scale factor of 2, centered at the origin where the endpoints are A (3,7) and B(4,9)
To find the coordinates of A' and B', we need to multiply the x and y values of A and B by the scale factor (2). Since the center of dilation is the origin (0, 0), we do not need to make any additional adjustments.
A' = (2 * x-coordinate of A, 2 * y-coordinate of A)
= (2 * 3, 2 * 7)
= (6, 14)
B' = (2 * x-coordinate of B, 2 * y-coordinate of B)
= (2 * 4, 2 * 9)
= (8, 18)
Therefore, A' = (6, 14) and B' = (8, 18)
To find the coordinates of the dilated points A' and B', we need to multiply the coordinates of points A and B by the scale factor of 2.
The formula to find the coordinates after dilation is:
(x', y') = (k * x, k * y),
Where (x, y) are the original coordinates, (x', y') are the new coordinates after dilation, and k is the scale factor.
Let's find the coordinates of point A' first:
Coordinate x of A':
x' = 2 * x = 2 * 3 = 6
Coordinate y of A':
y' = 2 * y = 2 * 7 = 14
So, the coordinates of point A' are (6, 14).
Now, let's find the coordinates of point B':
Coordinate x of B':
x' = 2 * x = 2 * 4 = 8
Coordinate y of B':
y' = 2 * y = 2 * 9 = 18
So, the coordinates of point B' are (8, 18).
Therefore, after dilation of the line segment AB with a scale factor of 2, the coordinates of A' are (6, 14) and the coordinates of B' are (8, 18).