1) If P'(2,-6) is the image of point P after the dilation D(to the 2nd power), what are the coordinates of point P?
2) A transformation maps (x,y) onto (x+2, y-1). Find the coordinates of A', the image of point A(-2,6) under the same transformation.
1) To find the coordinates of point P after the dilation, we need to understand the properties of dilation. A dilation is a transformation that changes the size of a figure, but not its shape. It is performed by multiplying the coordinates of each point by a scale factor.
Let's assume the scale factor of the dilation is "D". This means that if P'(2,-6) is the image of point P after the dilation, we can set up the following equation using the coordinates of P and P':
(x, y) * D = (2, -6)
To solve for (x, y), we need to divide both sides of the equation by D:
(x, y) = (2, -6) / D
Without more information about the scale factor D, we cannot determine the exact coordinates of point P. You will need to provide the value of D to find the coordinates of point P.
2) In this case, the transformation is defined as (x, y) --> (x+2, y-1). This means that to find the image of point A(-2, 6), we need to add 2 to the x-coordinate and subtract 1 from the y-coordinate.
A' = (-2 + 2, 6 - 1) = (0, 5)
Therefore, the coordinates of A' are (0, 5).