The vertices of a trapezoid are shown below. P(0, 0), Q(2, 0), R(2, 7), S(0, 14) This trapezoid is dilated about the origin by a scale factor of 5. What is the location of point S'?

So, point S seems to be the top left corner of a 4 sided trapezoid. If you graph this then it may be easier to imagine. Dilate means to get bigger, if you have trouble remembering this, think about how the pupil dilates when you’re in a dark room. (It gets bigger). So this shape is dilated about the origin which means that points that have 0’s in them now (for example (0,0) or (5,0) ) are only going to change for the number that isn’t a 0. So (0,0) dilated by any factor is still (0,0). But if a point was at (0,5) and dilated by a factor of 2, the new point would be (0,10). This is only the case if the shape is dilated around the origin. (Origin is at point (0,0) ). So point S we can see (0,14) has a 0 in it so we are only multiplying the 14 by the scale factor of 5. So 14 * 5 is 70. So the new location of S’ would be (0,70)

The density of the cube is 40