Question

This is the resulting picture of a flag after getting dilated about the origin by a scale factor of $0.5$. What were the original coordinates of the flag?

• A. $A(8,4),B(20,12),C(8,12)$
• B. $A(8,8),B(20,12),C(8,6)$
• C. $A(8,8),B(20,12),C(8,12)$
• D. $A(8,8),B(20,6),C(8,12)$

Answer 1

The correct option is C $A(8,8),B(20,12),C(8,12)$

Coordinates of the triangle after translation $=A^{\prime }(4,4),B^{\prime }(10,6),C^{\prime }(4,6)$

Let the initial coordinates of $A$ be $(x,y)$.
The triangle is dilated about the origin with a scale factor of $0.5$.
So, $A^{\prime }(x\times 0.5,y\times 0.5)\to A^{\prime }(4,4)$
This means, $x\times 0.5=4$.
$\Rightarrow x=4/0.5$
$\Rightarrow x=8$
Similarly, $y\times 0.5=4$.
$\Rightarrow y=4/0.5$
$\Rightarrow y=8$
Similarly, by dividing each coordinate of the vertices $B^{\prime }$ and $C$’ by $0.5$, we get $B(20,12)$ and $C(8,12)$.