The length of B'C' is calculated as: 8√10 units.
What is the length of the triangle after dilation?
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;
d = √[(y₂ - y₁)² + (x₂ - x₁)²
Where;
(x₁, y₁) = (4, 8)
(x₂, y₂) = (6, 2)
Substituting gives;
AB = √[(2 - 8)² + (6 - 4)²
AB = 2√10
Therefore, given that ΔA'B'C is created by dilating ΔABC by a scale factor of 4, the length of B'C' = 4 × The length of BC
Therefore, the length of B'C' = 4 × The length of BC = 4 × 2√10 = 8√10
The length of B'C' = 8√10 units.