Question

triangle mnp will be dilated according to the rule $d_{p,2}(x,y)$, where point p is the center of dilation.
what will be the coordinates of vertex n of the image?
$\circ$ (-2, 4)
$\circ$ (-2, 6)
$\circ$ (-4, 4)
$\circ$ (-4, 8)

Explanation:

Step1: Find coordinates of N and P

From the graph, \( N(0, 2) \) and \( P(2, -2) \). The dilation rule is \( D_{P,2}(x,y) \), meaning scale factor 2 with center P.

Step2: Use dilation formula

The formula for dilation with center \( (a,b) \) and scale factor \( k \) is \( (a + k(x - a), b + k(y - b)) \). Here, \( a = 2 \), \( b = -2 \), \( k = 2 \), \( x = 0 \), \( y = 2 \).
Substitute: \( x' = 2 + 2(0 - 2) = 2 - 4 = -2 \), \( y' = -2 + 2(2 - (-2)) = -2 + 2(4) = -2 + 8 = 6 \). So \( N'(-2, 6) \).

Answer:

\( \boldsymbol{(-2, 6)} \) (corresponding to the option: (-2, 6))