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

(D) 2

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 = \frac{Length \ of \overline {B'C'}}{Length \ of \overline {BC}} = \frac{Length \ of \overline {A'C'}}{Length \ of \overline {AC}} = \frac{Length \ of \overline {A'B'}}{Length \ of \overline {AB}}`

`\frac{Length \ of \overline {B'C'}}{Length \ of \overline {BC}} = (2 \ units)/(1 \ unit) = 2`

`\frac{Length \ of \overline {A'C'}}{Length \ of \overline {AC}} = (4 \ units)/(2 \ units) = 2`

`\frac{Length \ of \overline {A'B'}}{Length \ of \overline {AB}} = (2 \cdot √(5) \ units)/(√(5) \ units) = 2`

Therefore, the scale factor = 2