Triangle ABC with vertices at A(4, 3), B(3, −2), C(−3, 1) is dilated using a scale factor of 3.5 to create triangle A′B′C′. Determine the vertex of point C′.

Question

C′(−10.5, 1)
C′(−10.5, 3.5)
C′(−3, 3.5)
C′(−10.5, −3.5)

Answer 1

To find the coordinates of vertex C' after dilating point C(−3, 1) with a scale factor of 3.5, we need to use the formula for dilation:

\[ C' = (k \cdot x_C, k \cdot y_C) \]

where \(k\) is the scale factor, and \((x_C, y_C)\) are the coordinates of point C.

Here,

• \(k = 3.5\)
• \(C(-3, 1)\)

Now, we perform the dilation:

1. Calculate the x-coordinate of C': \[ x_{C'} = 3.5 \cdot (-3) = -10.5 \]

2. Calculate the y-coordinate of C': \[ y_{C'} = 3.5 \cdot 1 = 3.5 \]

Thus, the coordinates of point C' are: \[ C'(-10.5, 3.5) \]

The correct option is: \[ C'(-10.5, 3.5) \]