Question

Shape X is translated by (-2 5) to give shape Y. Shape Y is translated by (7 -3) to give shape Z. What is the translation from a) shape X to shape Z?

Answer 1

The overall translation from shape X to shape Z is calculated by adding the given translations component-wise, resulting in a total translation of (5, 2).

Step-by-step explanation:

The question involves understanding how translations work in geometry. To find the translation from shape X to shape Z, we must combine the two given translations: (-2, 5) for the translation from X to Y and (7, -3) for the translation from Y to Z. By adding these translations together component-wise, we get the total translation from shape X to shape Z.

For the x-component, we have -2 (from X to Y) and +7 (from Y to Z), which gives us a combined translation of -2 + 7 = 5 in the x-direction. For the y-component, we have +5 (from X to Y) and -3 (from Y to Z), which results in a combined translation of 5 - 3 = 2 in the y-direction. Therefore, the overall translation from shape X to shape Z is (5, 2).