Question

calculator
select from the drop-down menus to correctly complete each statement.
triangle abc can be mapped onto triangle def with
a reflection across the x-axis , followed by a
translation of 1 unit to the right and 3 units up, and a
dilation centered at the origin with a scale factor of
choose...

Explanation:

Step1: Analyze lengths of sides in triangle ABC

First, find the lengths of sides in triangle \(ABC\). Points \(A(-1,3)\), \(B(-4,3)\), \(C(-4,6)\).
Length of \(AB\): distance between \(A\) and \(B\). Since \(y\)-coordinates are same, \(AB = |-1 - (-4)| = 3\).
Length of \(BC\): distance between \(B\) and \(C\). Since \(x\)-coordinates are same, \(BC = |6 - 3| = 3\).

Step2: Analyze lengths of sides in triangle DEF

Points \(D(2,6)\), \(E(8,6)\), \(F(8,12)\).
Length of \(DE\): distance between \(D\) and \(E\). \(DE = |8 - 2| = 6\).
Length of \(EF\): distance between \(E\) and \(F\). \(EF = |12 - 6| = 6\).

Step3: Determine scale factor

Scale factor \(k\) is the ratio of corresponding side lengths (after reflection and translation).
Take \(AB\) and \(DE\): \(k=\frac{DE}{AB}=\frac{6}{3}=2\).
Or \(BC\) and \(EF\): \(k=\frac{EF}{BC}=\frac{6}{3}=2\).

Answer:

2