the graph shows quadrilaterals fghi and lmno. is fghi congruent to lmno? justify your answer. yes, because a…

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.

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.

Answer

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\neq LM). Congruent figures have all corresponding sides equal.

Answer:

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