Question

math journal jada will draw two scale drawings of the same object on 1 - cm grid paper. each centimeter will represent a greater distance in the second drawing than in the first. jada claims that the lengths in the second drawing will be longer than the lengths in the first drawing. do you agree? give an example of a scale and a measurement to support your answer.

Explanation:

Step1: Understand scale concept

The scale determines the relationship between the drawing and the actual object. A larger - scale factor means a smaller representation on the drawing.

Step2: Analyze Jada's claim

If each centimeter represents a greater distance in the second drawing, the scale of the second drawing is smaller. For example, if the first scale is 1 cm : 1 m (1:100) and the second scale is 1 cm : 2 m (1:200).
Let the actual length of the object be 4 m.
For the first scale 1 cm : 1 m, the length on the drawing is $\frac{4}{1}=4$ cm.
For the second scale 1 cm : 2 m, the length on the drawing is $\frac{4}{2}=2$ cm.

Answer:

No, I do not agree. For example, if the first scale is 1 cm represents 1 m and the second scale is 1 cm represents 2 m, and the actual length of an object is 4 m. In the first drawing, the length on the drawing is 4 cm, and in the second drawing, the length on the drawing is 2 cm.