Determine points S(-1,4), T(2,3), R(-1,0), and U(2,-1) after it has been dilated by k = 2
To dilate a point by a factor of k, we multiply the x and y coordinates of the point by k.
For point S(-1, 4), when dilated by k = 2:
x-coordinate: -1 * 2 = -2
y-coordinate: 4 * 2 = 8
So, the dilated coordinates of point S are (-2, 8).
For point T(2, 3), when dilated by k = 2:
x-coordinate: 2 * 2 = 4
y-coordinate: 3 * 2 = 6
So, the dilated coordinates of point T are (4, 6).
For point R(-1, 0), when dilated by k = 2:
x-coordinate: -1 * 2 = -2
y-coordinate: 0 * 2 = 0
So, the dilated coordinates of point R are (-2, 0).
For point U(2, -1), when dilated by k = 2:
x-coordinate: 2 * 2 = 4
y-coordinate: -1 * 2 = -2
So, the dilated coordinates of point U are (4, -2).
To dilate a point (x, y) by a scale factor k, we can multiply both the x and y coordinates by k.
Let's apply the dilation by k = 2 to the given points:
For point S(-1, 4):
The new x-coordinate is equal to -1 * 2 = -2
The new y-coordinate is equal to 4 * 2 = 8
So, after being dilated by k = 2, point S becomes S'(-2, 8).
For point T(2, 3):
The new x-coordinate is equal to 2 * 2 = 4
The new y-coordinate is equal to 3 * 2 = 6
So, after being dilated by k = 2, point T becomes T'(4, 6).
For point R(-1, 0):
The new x-coordinate is equal to -1 * 2 = -2
The new y-coordinate is equal to 0 * 2 = 0
So, after being dilated by k = 2, point R becomes R'(-2, 0).
For point U(2, -1):
The new x-coordinate is equal to 2 * 2 = 4
The new y-coordinate is equal to -1 * 2 = -2
So, after being dilated by k = 2, point U becomes U'(4, -2).
To summarize:
- S(-1, 4) dilated by k = 2 becomes S'(-2, 8).
- T(2, 3) dilated by k = 2 becomes T'(4, 6).
- R(-1, 0) dilated by k = 2 becomes R'(-2, 0).
- U(2, -1) dilated by k = 2 becomes U'(4, -2).
To determine the points after dilation, we need to multiply the coordinates of each point by the dilation factor, k.
Let's calculate the coordinates of each point after dilation:
For point S(-1, 4):
- Multiply the x-coordinate by k: -1 * 2 = -2
- Multiply the y-coordinate by k: 4 * 2 = 8
So, after dilation, point S becomes S'(-2, 8).
For point T(2, 3):
- Multiply the x-coordinate by k: 2 * 2 = 4
- Multiply the y-coordinate by k: 3 * 2 = 6
So, after dilation, point T becomes T'(4, 6).
For point R(-1, 0):
- Multiply the x-coordinate by k: -1 * 2 = -2
- Multiply the y-coordinate by k: 0 * 2 = 0
So, after dilation, point R becomes R'(-2, 0).
For point U(2, -1):
- Multiply the x-coordinate by k: 2 * 2 = 4
- Multiply the y-coordinate by k: -1 * 2 = -2
So, after dilation, point U becomes U'(4, -2).
Therefore, the new coordinates of the points after being dilated by k = 2 are:
- S'(-2, 8)
- T'(4, 6)
- R'(-2, 0)
- U'(4, -2)