Question

a dilation with a center at ( p(0,0) ) and a scale factor ( k ) is applied to ( overline{mn} ). let ( overline{mn} ) represent the image of ( overline{mn} ) after the dilation. select each correct statement. a if ( k>0 ), then ( mn>mn ) b if ( k>1 ), then ( mn>mn ). c if ( 0<k<1 ), then ( mn<mn ). d if ( 0.5<k<1.5 ), then ( mn<mn ) e if ( k = 1 ), then ( mn=mn ). f if ( k = 0.5 ), then ( mn=0.5(mn) )

Explanation:

Step1: Recall the property of dilation

When a dilation with center at the origin \((0,0)\) and scale factor \(k\) is applied to a line segment \(MN\), the length of the image segment \(M'N'\) is given by the formula \(M'N'=k\times MN\).

Step2: Analyze each option

• Option A: If \(k > 0\), when \(0 0\), then \(M'N'>MN\)” is False.
• Option B: If \(k>1\), then \(M'N'=k\times MN\). Since \(k > 1\), we have \(M'N'=k\times MN>MN\).
• Option C: If \(0 < k<1\), then \(M'N'=k\times MN\). Since \(0 < k<1\), we have \(M'N'=k\times MN
• Option D: If \(0.5 < k<1.5\), when \(0.5 < k<1\), \(M'N'=k\times MNMN\). So, the statement “If \(0.5 < k<1.5\), then \(M'N'
• Option E: If \(k = 1\), then \(M'N'=k\times MN=1\times MN = MN\).
• Option F: If \(k=0.5\), then \(M'N'=k\times MN=0.5\times MN\).

Answer:

B. If \(k > 1\), then \(M'N'>MN\); C. If \(0 < k<1\), then \(M'N'