Question

1. error analysis emilia was asked to find the coordinates of $d_2(\triangle abc)$ for $a(2, 4)$, $b(0, 5)$, and $c(-2, 1)$. what is emilia’s error?

$a(2, 4) \to a(4, 6)$
$b(0, 5) \to b(2, 7)$
$c(-2, 1) \to c(0, 3)$

Explanation:

Step1: Define dilation rule

A dilation \(D_k\) with scale factor \(k\) multiplies each coordinate of a point \((x,y)\) by \(k\): \((x,y) \to (kx, ky)\)

Step2: Calculate correct A'

For \(A(2,4)\) and \(k=2\):
\(A' = (2 \times 2, 2 \times 4) = (4, 8)\)

Step3: Calculate correct B'

For \(B(0,5)\) and \(k=2\):
\(B' = (2 \times 0, 2 \times 5) = (0, 10)\)

Step4: Calculate correct C'

For \(C(-2,1)\) and \(k=2\):
\(C' = (2 \times (-2), 2 \times 1) = (-4, 2)\)

Step5: Identify Emilia's error

Emilia added 2 to each coordinate instead of multiplying each coordinate by the scale factor 2.

Answer:

Emilia performed a translation (added 2 to each coordinate) instead of a dilation by scale factor 2 (which requires multiplying each coordinate by 2). The correct coordinates are \(A'(4,8)\), \(B'(0,10)\), and \(C'(-4,2)\).