Question

1.47 check your understanding
the diagram shows points b, b, and b.
what value can be multiplied to the length of bb to determine the length of bb?
4
5
8
10

Explanation:

Step1: Observe the scale - like relationship

Assume the points are on a line segment with a proportional relationship. If we consider the ratio of the lengths of the segments formed by the three collinear points \(B\), \(B'\), and \(B''\). Suppose the length of \(BB'\) is \(x\) and the length of \(BB''\) is \(y\). If we assume a dilation or a proportional growth from \(B\) to \(B'\) and then to \(B''\), by counting the grid - like units (assuming a uniform scale), we can see that the length of \(BB''\) is 4 times the length of \(BB'\).

Step2: Determine the multiplier

The multiplier \(k\) such that \(y = kx\). Since \(y\) (length of \(BB''\)) is 4 times \(x\) (length of \(BB'\)), \(k = 4\).

Answer:

4