Question

On a scale drawing of a table, the length is 12 units and the width is 8 units. Each unit on the grid represents 15 cm. Xavier says that if he draws another scale drawing of the table with a scale of 20 cm for each unit, it will be larger than the original drawing because 20 > 15. Explain why Xavier is incorrect with a drawing.

Answer 1

Xavier is incorrect because a larger scale factor does not necessarily mean a larger drawing. It all depends on the actual measurements that each unit represents.

Step-by-step explanation:

Xavier is incorrect because a larger scale factor means that each unit on the grid represents a larger measurement. In this case, the scale factor of 20 cm for each unit is actually smaller than the original scale factor of 15 cm for each unit. This means that each unit on the new scale drawing will be smaller than the units on the original drawing.

Let's take an example. In the original scale drawing, a length of 12 units represents 12 imes 15 cm = 180 cm. However, in the new scale drawing, a length of 12 units will represent 12 imes 20 cm = 240 cm. This shows that the new scale drawing is actually larger.

So, a larger scale factor does not necessarily mean a larger drawing. It all depends on the actual measurements that each unit represents.