Write the coordinates of the vertices after a dilation with a scale factor of 3, centered at the origin.

Question

Q
'
,
R
'
,
S
'
,

q = -1, -2
r= 0, -2
s = 1,1

Answer 1

To perform a dilation with a scale factor of 3 centered at the origin, you multiply the coordinates of each vertex by the scale factor.

Given the original coordinates:

• \( Q(-1, -2) \)
• \( R(0, -2) \)
• \( S(1, 1) \)

We apply the dilation:

1. For \( Q' \): \[ Q' = (3 \cdot -1, 3 \cdot -2) = (-3, -6) \]

2. For \( R' \): \[ R' = (3 \cdot 0, 3 \cdot -2) = (0, -6) \]

3. For \( S' \): \[ S' = (3 \cdot 1, 3 \cdot 1) = (3, 3) \]

So the coordinates of the vertices after the dilation are:

• \( Q'(-3, -6) \)
• \( R'(0, -6) \)
• \( S'(3, 3) \)