Question

1. trapezoid rain has vertices r(-2,1), a(1,1), i(0,-1), and n(-1,-1). graph the image of the figure after a dilation with a scale factor of 2. (example 1)
2. triangle jkl has vertices j(-4,-1), k(0,4), and l(-4,-2). graph the image of the figure after a dilation with a scale factor of 0.5. (example 2)

Explanation:

Problem 1: Trapezoid RAIN Dilation (Scale Factor 2)

Step1: Recall Dilation Rule

For a dilation with scale factor \( k \) centered at the origin \((0,0)\), the new coordinates \((x', y')\) of a point \((x, y)\) are given by \( (x', y')=(k \cdot x, k \cdot y) \).

Step2: Find New Coordinates for R, A, I, N

• For \( R(-2, 1) \):

\( x' = 2 \times (-2)= -4 \), \( y' = 2 \times 1 = 2 \). So \( R'(-4, 2) \).

• For \( A(1, 1) \):

\( x' = 2 \times 1 = 2 \), \( y' = 2 \times 1 = 2 \). So \( A'(2, 2) \).

• For \( I(0, -1) \):

\( x' = 2 \times 0 = 0 \), \( y' = 2 \times (-1)= -2 \). So \( I'(0, -2) \).

• For \( N(-1, -1) \):

\( x' = 2 \times (-1)= -2 \), \( y' = 2 \times (-1)= -2 \). So \( N'(-2, -2) \).

Step3: Graph the Image

Plot the new vertices \( R'(-4, 2) \), \( A'(2, 2) \), \( I'(0, -2) \), \( N'(-2, -2) \) and connect them to form the dilated trapezoid.

Problem 3: Triangle JKL Dilation (Scale Factor 0.5)

Step1: Recall Dilation Rule

For a dilation with scale factor \( k = 0.5 \) centered at the origin, the new coordinates \((x', y')\) of a point \((x, y)\) are \( (x', y')=(0.5 \cdot x, 0.5 \cdot y) \).

Step2: Find New Coordinates for J, K, L

• For \( J(-4, -1) \):

\( x' = 0.5 \times (-4)= -2 \), \( y' = 0.5 \times (-1)= -0.5 \). So \( J'(-2, -0.5) \).

• For \( K(0, 4) \):

\( x' = 0.5 \times 0 = 0 \), \( y' = 0.5 \times 4 = 2 \). So \( K'(0, 2) \).

• For \( L(-4, -2) \):

\( x' = 0.5 \times (-4)= -2 \), \( y' = 0.5 \times (-2)= -1 \). So \( L'(-2, -1) \).

Step3: Graph the Image

Plot the new vertices \( J'(-2, -0.5) \), \( K'(0, 2) \), \( L'(-2, -1) \) and connect them to form the dilated triangle.

Answer:

(Graphing Instructions):

1. For trapezoid RAIN (scale factor 2): Plot \( R'(-4, 2) \), \( A'(2, 2) \), \( I'(0, -2) \), \( N'(-2, -2) \) and connect.
2. For triangle JKL (scale factor 0.5): Plot \( J'(-2, -0.5) \), \( K'(0, 2) \), \( L'(-2, -1) \) and connect.

(Note: Graphing involves plotting these points on a coordinate plane and drawing the shapes.)