Answer:
Option B
Step-by-step explanation:
It's clear from the graph attached,
ΔABC has been dilated and shifted downwards.
Length of segment AB = 2 units
Length of segment DE = 4 units
Scale factor by which the dilation has been done = [tex]\frac{\text{Dimension of the image triangle}}{\text{Dimension of the original triangle}}[/tex]
Scale factor = [tex]\frac{DE}{AB}[/tex]
= [tex]\frac{4}{2}[/tex]
= 2
Therefore, triangle ABC is dilated by a scale factor of 2 about the origin.
Lets consider a point B(0, 0) from the given graph and analyze the transformations done.
If a point B(0, 0) is shifted to point E(0, -10) which follows the rule,
B(0, 0) → E(0 + h, 0 + k)
Here, 'h' and 'k' are the translations of the given point over x-axis and y-axis.
Therefore, (0 + h) = 0 ⇒ h = 0
0 + k = -10
k = -10
Hence, triangle ABC has been dilated by a scale factor of 2 centered at origin and followed by the translation (x, y - 10)
Option B is the correct option.
