Answer:
The length of AB is 20 units
Step-by-step explanation:
The given parameters from the graph for coordinates A and B are;
The coordinates of the point A = (1, 4)
The coordinates of the point B = (4, 8)
The length of segment AB is given by the equation for finding the distance, d between two points given their coordinates as follows;
[tex]d = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
Where;
(x₁, y₁) = (1, 4)
(x₂, y₂) = (4, 8)
Substituting gives;
[tex]d_{AB} = \sqrt{\left (8-4 \right )^{2}+\left (4-1 \right )^{2}} = \sqrt{25} = 5[/tex]
The length of [tex]\overline {AB}[/tex] = 5
Therefore, given that ΔA'B'C is created by dilating ΔABC by a scale factor of 4, the length of A'B' = 4 × The length of AB
Therefore, the length of [tex]\overline {A'B'}[/tex] = 4 × The length of [tex]\overline {AB}[/tex] = 4 × 5 = 20
The length of [tex]\overline {A'B'}[/tex] = 20 units.
