Question

write a coordinate rule that describes the dilation ( d_3(\triangle pqr) ). use this rule to find the images of the vertices of ( \triangle pqr ) for this dilation. then graph the image.
the coordinate rule is ( d_3(x,y) = (3x,3y) ). (type an ordered pair.)
find the coordinates of the images.
the image of ( p ) is at (square).
the image of ( q ) is at (square).
the image of ( r ) is at (square).
(type ordered pairs. simplify your answers.)

Explanation:

Step1: Find coordinates of P, Q, R

From the graph, we can see:

• Coordinates of \( P \): Let's assume the grid has x and y axes. Looking at the graph, \( P \) is at \( (-1, 4) \) (since x = -1, y = 4)
• Coordinates of \( Q \): \( (3, 1) \) (x = 3, y = 1)
• Coordinates of \( R \): \( (-4, -3) \) (x = -4, y = -3)

Step2: Apply dilation rule \( D_3(x, y) = (3x, 3y) \) to each point

For point \( P(-1, 4) \):

Multiply x-coordinate by 3: \( 3\times(-1) = -3 \)
Multiply y-coordinate by 3: \( 3\times4 = 12 \)
So, image of \( P \) is \( (-3, 12) \)

For point \( Q(3, 1) \):

Multiply x-coordinate by 3: \( 3\times3 = 9 \)
Multiply y-coordinate by 3: \( 3\times1 = 3 \)
So, image of \( Q \) is \( (9, 3) \)

For point \( R(-4, -3) \):

Multiply x-coordinate by 3: \( 3\times(-4) = -12 \)
Multiply y-coordinate by 3: \( 3\times(-3) = -9 \)
So, image of \( R \) is \( (-12, -9) \)

Answer:

The image of \( P \) is at \((-3, 12)\), the image of \( Q \) is at \((9, 3)\), the image of \( R \) is at \((-12, -9)\)