Triangle qrs is dilated according to the rule do,2 (x, y). what is true about the image △q'r's'? check all that apply. do,2 (x, y) = (2x, 2y) side q's' lies on a line with a slope of -1. qr is longer than q'r'. the vertices of the image are closer to the origin than those of the pre-image. the distance from q' to the origin is twice the distance from q to the origin.

A dilation is a transformation, with center O and a scale factor of k that is not zero, that maps O to itself and any other point P to P'. The center O is a fixed point, P' is the image of P, points O, P and P' are on the same line.

Thus, a dilation of is a dilation with centre O and a scale factor of 2 mapping the original figure to the image in such a way that the distances from O to the vertices of the image are twice the distances from O to the original figure. Also the size of the image are twice the size of the original figure.

In the dilation of triangle QRS with the rule ,
1.) The size of the image △Q'R'S' is twice the size of △QRS (i.e. .
Thus the first option is true.

2.) Line Q'S' will lie on the same line as line QS. The slope of line QS = (3 - 1) / (-3 - (-1)) = 2 / -2 = -1.
Thus the second option is true.

3.) QR cannot be longer than Q'R' as the size of the image is twice the size of the original figure.
Thus the third option is not true.

4.) The vertices of the image cannot be closer to the origin than those of the pre-image as the distances from O to the vertices of the image are twice the distances from O to the original figure.
Thus the fourth option is not true.

5.) The distance from Q' to the origin is twice the distance from Q to the origin as the distances from O to the vertices of the image are twice the distances from O to the original figure.
Thus the fifth option is true.