Question

the graph shows quadrilaterals fghi and lmno. is fghi congruent to lmno? justify your answer. yes, because a translation right 12 units maps fghi onto lmno. yes, because a reflection across the y - axis maps fghi onto lmno. no, because \\( \overline { fg } \\) and \\( \overline { lm } \\) do not have the same length. no, because \\( \angle h \\) and \\( \angle n \\) do not have the same measure.

Explanation:

Step1: Calculate the length of \(FG\)

Using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For \(F(-8,8)\) and \(G(-7,5)\), \(d_{FG}=\sqrt{(-7+8)^2+(5 - 8)^2}=\sqrt{1 + 9}=\sqrt{10}\)

Step2: Calculate the length of \(LM\)

For \(L(8,7)\) and \(M(7,5)\), \(d_{LM}=\sqrt{(7 - 8)^2+(5 - 7)^2}=\sqrt{1+4}=\sqrt{5}\)

Since \(FG=\sqrt{10}\) and \(LM = \sqrt{5}\), \(FG
eq LM\). Congruent figures have all corresponding sides equal.

Answer:

No, because \(\overline{FG}\) and \(\overline{LM}\) do not have the same length.