Question

qusai made a scaled copy of the following trapezoid. he used a scale factor less than 1. what could be the length of the longer base of the scaled copy of the trapezoid? choose 3 answers: a 0.75 units

Explanation:

1. First, assume the length of the longer - base of the original trapezoid is \(b\) (let's say by counting the grid units, if the original longer - base has a length of \(3\) units for example).

• When we create a scaled copy with a scale factor \(k\lt1\), the length of the corresponding side of the scaled copy, \(b'\), is given by the formula \(b' = k\times b\).
• Since \(k\lt1\), the length of the longer - base of the scaled copy will be less than the length of the longer - base of the original trapezoid.

1. Analyze each option:

• Option A: If the original longer - base has a length greater than \(0.75\) units and the scale factor \(k\lt1\), \(0.75\) units could be the length of the longer - base of the scaled copy.
• Let's assume other possible values. If the original longer - base is \(4\) units, and the scale factor \(k = 0.5\), the length of the longer - base of the scaled copy is \(4\times0.5=2\) units. If \(k = 0.25\), the length of the longer - base of the scaled copy is \(4\times0.25 = 1\) unit.

Answer:

A. 0.75 units (assuming the original longer - base is long enough and the scale factor is appropriate), other possible answers could be values less than the length of the original longer - base such as 1 unit, 1.5 units etc. (depending on the original length and the scale factor). Since we need to choose 3 answers, without knowing the original length, we can just assume some values less than a reasonable original length. For example, if we assume the original length is 3 units, possible answers could be A. 0.75 units, 1 unit, 1.5 units. But we need the full set of options to give a definite 3 - answer set. If the other options include values less than the original length of the longer - base of the trapezoid, they would be correct.