Draw and translate simple shapes 5 - Reasoning

In a Geometry lesson focused on Position and Direction for Year 6, Malachi and Zach are presented with a challenge involving the translation of shape ABCD on a coordinate grid. They aim to move the shape so that the coordinates of point B become (5,2). Malachi suggests that after the translation, the coordinates of point D will be (-1,1), while Zach proposes that they will be (4,-1). However, the correct answer is that neither of them is right. The actual coordinates of point D after the translation will be (1,-1).

To determine who is correct, one must understand the concept of translation on a coordinate grid. Translation involves moving a shape a certain distance in a specific direction without rotating it. When translating shape ABCD so that point B lands on (5,2), the entire shape shifts in such a way that the relative positions of all points remain the same. To find the new coordinates of point D, one must apply the same horizontal and vertical changes that were applied to point B. After the correct translation, the coordinates of point D do not match either Malachi's or Zach's predictions, but instead, they end up being (1,-1), indicating that the shape has been moved correctly according to the rules of translation in a coordinate plane.