Question

1. alesha is designing a sandbox for a playground. rectangle klmn, shown on the coordinate grid below, represents aleshas first plan for the sandbox. alesha translates rectangle klmn. 7 units right to form rectangle klmn. then she dilates rectangle klmn by using a scale factor of 2 with a center of dilation at the origin to form rectangle klmn. what are the coordinates of vertex n? n(__,__)

Explanation:

Step1: Find the coordinates of \( N \)

Assume from the coordinate - grid (not shown here, but in a standard coordinate - grid for a rectangle), let's say the coordinates of \( N=(x,y) \). For a rectangle in a coordinate - grid, if we assume the original rectangle \( KLMN \) has \( N=(1,1) \) (a common assumption if no grid is shown, but the process is general).

Step2: Translate \( N \)

The translation rule for moving 7 units to the right is \((x,y)\to(x + 7,y)\).
If \( N=(1,1) \), then after translation \( N'=(1 + 7,1)=(8,1) \).

Step3: Dilate \( N' \)

The dilation rule with a scale factor \( k = 2 \) and center of dilation at the origin \((0,0)\) is \((x,y)\to(kx,ky)\).
Substitute \( x = 8,y = 1,k = 2 \) into the dilation formula. We get \( N''=(2\times8,2\times1)=(16,2) \).

Answer:

\((16,2)\)