Question

triangle mnp is dilated according to the rule ( d_{0,1.5}(x,y)\to(1.5x,1.5y) ) to create the image triangle ( mnp ), which is not shown. what are the coordinates of the endpoints of segment ( mn )? ( m(-6,9) ) and ( n(4,9) ) ( m(-6,9) ) and ( n(3,9) ) ( m(-2,3) ) and ( n(7,9) ) ( m(-2,3) ) and ( n(1,3) )

Explanation:

Step1: Find the coordinates of \(M\) and \(N\)

From the graph, the coordinates of \(M\) are \((- 4,6)\) and the coordinates of \(N\) are \((2,6)\)

Step2: Apply the dilation rule \(D_{0,1.5}(x,y)\to(1.5x,1.5y)\)

For point \(M(-4,6)\):
\(x = - 4,y = 6\)
After dilation, \(x'=1.5\times(-4)=-6\), \(y'=1.5\times6 = 9\)
So \(M'(-6,9)\)
For point \(N(2,6)\):
\(x = 2,y = 6\)
After dilation, \(x'=1.5\times2 = 3\), \(y'=1.5\times6=9\)
So \(N'(3,9)\)

Answer:

\(M'(-6,9)\) and \(N'(3,9)\) (corresponding to the second option \(M'(-6,9)\) and \(N'(3,9)\))