Question

Triangle RST has vertices R(0,0), S(6,3), and T(3,-3). Triangle R'S'T' is the image of triangle RST after a dilation with center (0,0) and a scale factor of 1/3. What are the coordinates of point S'?

Answer 1

Notice that the triangle has vertices (0, 0), (6, 3), and (3, -3), and we are asked to find the image of a dilation with center (0, 0) and scale factor 1/3. Since the (0, 0) is in fact one of the vertices of the original triangle, then we know that the image of the other two vertices will be on the segment that joins (0, 0) with each of the vertices.

In particular we are asked for the coordinates of point S' that derives from point S = (6, 3)

Notice that 1/3 of 6 is "2", and 1/3 of 3 is "1", therefore the point S' would be located at: (2, 1)