Question

dilate by a scale factor of 3. what is the location of the new point j?

Explanation:

Step1: Find coordinates of J

From the grid, point J has coordinates \((3, 2)\) (assuming each grid square is 1 unit; L is at (1,1), K at (3,1), M at (1,2), so J is at (3,2)).

Step2: Apply dilation formula

Dilation with scale factor \(k\) about the origin: \((x, y) \to (k \cdot x, k \cdot y)\). Here, \(k = 3\), so for \(J(3, 2)\), new coordinates \(J'\) are \((3 \times 3, 3 \times 2)\).

Step3: Calculate new coordinates

\(3 \times 3 = 9\), \(3 \times 2 = 6\). So \(J'\) is \((9, 6)\).

Answer:

\((9, 6)\)