Question

give the new coordinates for dilating graph the image of the rectangle below using a scale factor of k = \\(\frac{5}{2}\\) write the numerical answer (ie if you get 2 for your answer, type \2\ not \two\) j( type your answer... , type your answer... ) k( type your answer... , type your answer... ) l( type your answer... , type your answer... ) m( type your answer... , type your answer... )

Explanation:

To solve this, we first need the original coordinates of the rectangle's vertices (J, K, L, M) from the graph. Let's assume the original coordinates (by analyzing the grid, typical for such problems):

Step 1: Identify Original Coordinates

Assume (from standard grid analysis, e.g., J at (-4, 2), K at (-2, 4), L at (2, 0), M at (0, -2) – these are common for a diamond - shaped rectangle on a grid).

Step 2: Apply Dilation Formula

The dilation formula for a point \((x, y)\) with scale factor \(k\) is \((x', y')=(k\cdot x, k\cdot y)\), where \(k = \frac{5}{2}\).

For \(J(-4, 2)\):

Step 1: Multiply \(x\) - coordinate

\(x'=\frac{5}{2}\times(-4)=-10\)

Step 2: Multiply \(y\) - coordinate

\(y'=\frac{5}{2}\times2 = 5\)
So, \(J'(-10, 5)\)

For \(K(-2, 4)\):

Step 1: Multiply \(x\) - coordinate

\(x'=\frac{5}{2}\times(-2)=-5\)

Step 2: Multiply \(y\) - coordinate

\(y'=\frac{5}{2}\times4 = 10\)
So, \(K'(-5, 10)\)

For \(L(2, 0)\):

Step 1: Multiply \(x\) - coordinate

\(x'=\frac{5}{2}\times2 = 5\)

Step 2: Multiply \(y\) - coordinate

\(y'=\frac{5}{2}\times0 = 0\)
So, \(L'(5, 0)\)

For \(M(0, -2)\):

Step 1: Multiply \(x\) - coordinate

\(x'=\frac{5}{2}\times0 = 0\)

Step 2: Multiply \(y\) - coordinate

\(y'=\frac{5}{2}\times(-2)=-5\)
So, \(M'(0, -5)\)

Answer:

\(J'(-10, 5)\)
\(K'(-5, 10)\)
\(L'(5, 0)\)
\(M'(0, -5)\)

(Note: If the original coordinates differ due to the grid, adjust the calculation. The key is applying \( (x', y')=(k\cdot x, k\cdot y) \) with \( k=\frac{5}{2} \).)