X(-1,-2),Y(2,1),Z(4,-1); scale factor 3
To find the coordinates of the points X, Y, and Z after the scale factor of 3 is applied, you need to multiply each coordinate of the original point by the scale factor.
Let's start with point X(-1, -2). To scale it by a factor of 3, you'll multiply each coordinate by 3:
New X-coordinate = -1 * 3 = -3
New Y-coordinate = -2 * 3 = -6
So the new coordinates of point X after scaling are X'(-3, -6).
Next, let's consider point Y(2, 1). Applying the scale factor of 3 gives us:
New X-coordinate = 2 * 3 = 6
New Y-coordinate = 1 * 3 = 3
Thus, the new coordinates of point Y after scaling are Y'(6, 3).
Finally, let's calculate the new coordinates for point Z(4, -1):
New X-coordinate = 4 * 3 = 12
New Y-coordinate = -1 * 3 = -3
Therefore, the new coordinates of point Z after scaling are Z'(12, -3).
In summary, after scaling each point X, Y, and Z by a scale factor of 3, the new coordinates are:
X'(-3, -6)
Y'(6, 3)
Z'(12, -3)