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?
options:
m (-2, 3) and n (7, 9)
m (-6, 9) and n (3, 9)
m (-6, 9) and n (4, 9)
m (-2, 3) and n (1, 3)

Explanation:

Step1: Find coordinates of M and N

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

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

For \( M(-4, 6) \):
\( x' = 1.5 \times (-4) = -6 \), \( y' = 1.5 \times 6 = 9 \), so \( M'(-6, 9) \).
For \( N(2, 6) \):
\( x' = 1.5 \times 2 = 3 \), \( y' = 1.5 \times 6 = 9 \), so \( N'(3, 9) \).

Answer:

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