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 and N

From the graph, \( M(-4,6) \) and \( N(2,6) \).

Step2: Apply dilation rule

For point \( M \):
Using \( D_{O,1.5}(x,y)\to(1.5x,1.5y) \),
\( x = - 4,y = 6 \),
\( 1.5x=1.5\times(-4)=-6 \),
\( 1.5y=1.5\times6 = 9 \), so \( M'(-6,9) \).
For point \( N \):
\( x = 2,y = 6 \),
\( 1.5x=1.5\times2 = 3 \),
\( 1.5y=1.5\times6=9 \), so \( N'(3,9) \).

Answer:

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