Question

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

Explanation:

Step1: Determine coordinates of M and N

From the graph, \(M(-4,6)\) and \(N(\frac{8}{3},6)\)

Step2: Apply dilation rule \(D_{O,1.5}(x,y)=(1.5x,1.5y)\)

For \(M(-4,6)\):
\(x = 1.5\times(-4)=-6\), \(y = 1.5\times6 = 9\), so \(M'(-6,9)\)
For \(N(\frac{8}{3},6)\):
\(x=1.5\times\frac{8}{3}=4\), \(y = 1.5\times6=9\), so \(N'(4,9)\)

Answer:

M'(-6, 9) and N'(4, 9)