Question

graph the image of $\triangle tuv$ after a dilation with a scale factor of 3, centered at the origin.

Explanation:

Step1: Identify original coordinates

From graph: \( T(-4, -1) \), \( U(3, -1) \), \( V(-4, 2) \)

Step2: Apply dilation (scale factor 3)

Multiply each coordinate by 3:
\( T' = (-4×3, -1×3) = (-12, -3) \)
\( U' = (3×3, -1×3) = (9, -3) \)
\( V' = (-4×3, 2×3) = (-12, 6) \)

Step3: Plot new triangle

Connect \( T'(-12,-3) \), \( U'(9,-3) \), \( V'(-12,6) \)

Answer:

The image of \( \triangle TUV \) after dilation has vertices \( T'(-12, -3) \), \( U'(9, -3) \), \( V'(-12, 6) \). Plot these points and connect them to form the dilated triangle.