Respuesta :
Answer with explanation:
⇒Vertices of Δ PQR = P(2, 4), Q(3, 8) and R(5, 4)
Area of Δ PQR
[tex]=\frac{1}{2} \times \left[\begin{array}{ccc}2&4&1\\3&8&1\\5&4&1\end{array}\right] \\\\=\frac{1}{2} \times[ 2\times(8-4)-4 \times (3-5)+1 \times (12-40)]\\\\=\frac{1}{2} \times [8+8-28]\\\\=\frac{1}{2} \times|16-28|\\\\=\frac{1}{2} \times 12\\\\=6 \text{square units}[/tex]
⇒Vertices of Δ ABC A(2, 4), B(5.5, 18), and C(12.5, 4).
Area of Δ ABC
[tex]=\frac{1}{2} \times \left[\begin{array}{ccc}2&4&1\\5.5&18&1\\12.5&4&1\end{array}\right] \\\\=\frac{1}{2} \times[ 2\times(18-4)-4\times (5.5-12.5)+1 \times (22-225)]\\\\=\frac{1}{2} \times [28+28-203]\\\\=\frac{1}{2} \times|56-203|\\\\=\frac{1}{2} \times 147\\\\=73.50\text{square units}[/tex]
⇒Scale Factor or Dilation in this transformation
= is Area of Image Divided by Area of Preimage
[tex]=\frac{\text{Area of} \Delta ABC}{\text{Area of} \Delta PQR}\\\\=\frac{73.50}{6}\\\\=12.25[/tex]
