Question

triangle mnp is dilated according to the rule ( d_{o,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 coordinates of M

From the graph, \(M(-4,6)\).
Using dilation rule \(D_{O,1.5}(x,y)\to(1.5x,1.5y)\), for \(M\):
\(x = - 4,y = 6\)
\(1.5x=1.5\times(-4)=-6\)
\(1.5y = 1.5\times6 = 9\)
So \(M'(-6,9)\)

Step2: Find coordinates of N

From the graph, \(N(2,6)\).
Using dilation rule \(D_{O,1.5}(x,y)\to(1.5x,1.5y)\), for \(N\):
\(x = 2,y = 6\)
\(1.5x=1.5\times2 = 3\)
\(1.5y=1.5\times6 = 9\)
So \(N'(3,9)\)

Answer:

M'(-6, 9) and N'(3, 9)