Question

OAA', OBB', and OCC' are straight lines. Triangle ABC is mapped onto Triangle A'B'C' by an enlargement with center O. What is the scale factor of enlargement.​

Answer 1

Answer:

(D) 2

Step-by-step explanation:

The scale factor of the enlargement of ΔABC to ΔA'B'C' is given by the ratio of the length of the corresponding sides of ΔA'B'C' and ΔABC

Therefore, we have;

$The \ scale \ factor = \dfrac{Length \ of \overline {B'C'}}{Length \ of \overline {BC}} = \dfrac{Length \ of \overline {A'C'}}{Length \ of \overline {AC}} = \dfrac{Length \ of \overline {A'B'}}{Length \ of \overline {AB}}$

$\dfrac{Length \ of \overline {B'C'}}{Length \ of \overline {BC}} = \dfrac{2 \ units}{1 \ unit} = 2$

$\dfrac{Length \ of \overline {A'C'}}{Length \ of \overline {AC}} = \dfrac{4 \ units}{2 \ units} = 2$

$\dfrac{Length \ of \overline {A'B'}}{Length \ of \overline {AB}} = \dfrac{2 \cdot \sqrt{5} \ units}{\sqrt{5} \ units} = 2$

Therefore, the scale factor = 2