Question

1. 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 dilation formula

The length of the image \(M'N'\) after dilation with scale factor \(k\) is \(M'N'=k\times MN\).

Step2: Analyze each option

• Option A: If \(k > 0\), when \(01\), \(M'N'>MN\). So the statement “If \(k > 0\), then \(M'N'>MN\)” is False.
• Option B: If \(k>1\), using the formula \(M'N'=k\times MN\), since \(k > 1\), we have \(M'N'=k\times MN>MN\). This statement is True.
• Option C: If \(0 < k<1\), by the formula \(M'N'=k\times MN\), we get \(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 \(M'N'=1\times MN=MN\). This statement is True.
• Option F: If \(k = 0.5\), then \(M'N'=0.5\times MN\). This statement is True.

Answer:

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