Math topic中文

Homothety in the coordinate plane

In the Cartesian plane, explore that scaling all vertex coordinates of a polygon (with one vertex at the origin) by the same factor produces a figure homothetic to the original.

Practice questions

  1. 1以原点O为位似中心，将△AOB放大到原来的2倍，若点A的坐标为（2，3），则点A的对应点A′的坐标为___．
  2. 2在平面直角坐标系中，已知点E(−4,2)E(-4,2)，F(−2,−2)F(-2,-2)，以原点OO为位似中心，相似比为1﹕21﹕2，把△EFO\triangle EFO缩小，则点EE的对应点E′E′的坐标是 ___ ．