Question

the vertices of triangle abc are a(2,3), b(-1,2), and c(3,1). if adef - aabc and de = 4ab, what is the length of ef?
o √10
o √17
o 4√10
o 4√17

Explanation:

Step1: Calculate the length of \(AB\)

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For \(A(2,3)\) and \(B(-1,2)\), \(x_1 = 2,y_1 = 3,x_2=-1,y_2 = 2\).

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Step2: Find the length of \(DE\)

Since \(DE = 4AB\), substitute \(AB=\sqrt{10}\) into the equation.
\(DE=4\sqrt{10}\)

Answer:

\(4\sqrt{10}\)