Given a scale factor of 2, find a coordinates for the dilation of the line segment with endpoints (-1,2) and (3,-3)
To find the dilation of a line segment, we multiply the distance between the endpoints by the scale factor and then add the result to the x-coordinate of the first endpoint to get the x-coordinate of the new endpoint, and we do the same thing for the y-coordinate.
For the x-coordinate of the new endpoint, we have:
-1 + 2(3 - (-1)) = -1 + 2(4) = 7
For the y-coordinate of the new endpoint, we have:
2 + 2(-3 - 2) = 2 + 2(-5) = -8
Therefore, the dilation of the line segment with endpoints (-1,2) and (3,-3) with a scale factor of 2 is (-1,2) -> (7,-8).
To find the coordinates of the dilation of the line segment with endpoints (-1,2) and (3,-3) using a scale factor of 2, follow these steps:
1. Calculate the difference between the x-coordinates of the endpoints:
Δx = x₂ - x₁ = 3 - (-1) = 4
2. Calculate the difference between the y-coordinates of the endpoints:
Δy = y₂ - y₁ = (-3) - 2 = -5
3. Multiply the difference in x-coordinates by the scale factor:
Δx' = 2 * Δx = 2 * 4 = 8
4. Multiply the difference in y-coordinates by the scale factor:
Δy' = 2 * Δy = 2 * (-5) = -10
5. Add the scaled differences to the x-coordinate of the first endpoint to find the x-coordinate of the dilated endpoint:
x' = x₁ + Δx' = -1 + 8 = 7
6. Add the scaled differences to the y-coordinate of the first endpoint to find the y-coordinate of the dilated endpoint:
y' = y₁ + Δy' = 2 + (-10) = -8
Therefore, the coordinates of the dilation of the line segment with endpoints (-1,2) and (3,-3), using a scale factor of 2, are (7, -8).